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Título : Buildings, Finite Geometries and Groups : Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Sastry, N.S. Narasimha Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Colección: Springer Proceedings in Mathematics, ISSN 2190-5614 num. 10 Número de páginas: XII, 344 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-0709-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Manifolds (Mathematics) Complex manifolds Geometry and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This volume collects articles inspired by the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, from August 29 – 31, 2010. These contributors include some of the most active researchers in areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, and more. Contributions reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective that the authors bring to their articles on current developments and major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these fields Nota de contenido: 1. On Characterizing Designs By Their Codes (B. Bagchi) -- 2. The Geometry of Extremal Elements in a Lie Algebra (A.M. Cohen) -- 3. Properties of a 27-dimensional Space of Symmetric Bilinear Forms Acted on by E6 (R. Gow) -- 4. On the Geometry of Global Function Fields, the Riemann-Roch Theorem, and Finiteness Properties of S-arithmetic Groups (R. Gramlich) -- 5. Some Remarks on Two-Transitive Permutation Groups as Multiplication Groups of Quasigroups (G. Hiss, F. Lübeck) -- 6. Curve Complexes Versus Tits Buildings: Structures and Applications (Lizhen Ji) -- 7. On Isotypies Between Galois Conjugate Blocks (R. Kessar) -- 8. Representations of Unitriangular Groups (T. Le, K. Magaard) -- 9. Hermitian Vernonesean Caps (J. Schillewaert, H. Van Maldeghem) -- 10. On a Class of c.F4-geometries (A. Pasini) -- 11. Buildings and Kac-Moody Groups (B. Rémy) -- 12. Some Equations Over Finite Fields Related to Simple Groups of Suzuki and Ree Types (N.S. Narasimha Sastry) -- 13. Oppositeness in Buildings and Simple Modules for Finite Groups of Lie Type (P. Sin) -- 14. Modular Representations, Old and New (B. Srinivasan) -- 15. The Use of Blocking Sets in Galois Geometries and in Related Research Areas (V. Pepe, L. Storme) -- 16. Quadratic Actions (F.G. Timmesfeld) -- Problem Set.- En línea: http://dx.doi.org/10.1007/978-1-4614-0709-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32743 Buildings, Finite Geometries and Groups : Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010 [documento electrónico] / SpringerLink (Online service) ; Sastry, N.S. Narasimha . - New York, NY : Springer New York, 2012 . - XII, 344 p : online resource. - (Springer Proceedings in Mathematics, ISSN 2190-5614; 10) .
ISBN : 978-1-4614-0709-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Manifolds (Mathematics) Complex manifolds Geometry and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This volume collects articles inspired by the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, from August 29 – 31, 2010. These contributors include some of the most active researchers in areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, and more. Contributions reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective that the authors bring to their articles on current developments and major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these fields Nota de contenido: 1. On Characterizing Designs By Their Codes (B. Bagchi) -- 2. The Geometry of Extremal Elements in a Lie Algebra (A.M. Cohen) -- 3. Properties of a 27-dimensional Space of Symmetric Bilinear Forms Acted on by E6 (R. Gow) -- 4. On the Geometry of Global Function Fields, the Riemann-Roch Theorem, and Finiteness Properties of S-arithmetic Groups (R. Gramlich) -- 5. Some Remarks on Two-Transitive Permutation Groups as Multiplication Groups of Quasigroups (G. Hiss, F. Lübeck) -- 6. Curve Complexes Versus Tits Buildings: Structures and Applications (Lizhen Ji) -- 7. On Isotypies Between Galois Conjugate Blocks (R. Kessar) -- 8. Representations of Unitriangular Groups (T. Le, K. Magaard) -- 9. Hermitian Vernonesean Caps (J. Schillewaert, H. Van Maldeghem) -- 10. On a Class of c.F4-geometries (A. Pasini) -- 11. Buildings and Kac-Moody Groups (B. Rémy) -- 12. Some Equations Over Finite Fields Related to Simple Groups of Suzuki and Ree Types (N.S. Narasimha Sastry) -- 13. Oppositeness in Buildings and Simple Modules for Finite Groups of Lie Type (P. Sin) -- 14. Modular Representations, Old and New (B. Srinivasan) -- 15. The Use of Blocking Sets in Galois Geometries and in Related Research Areas (V. Pepe, L. Storme) -- 16. Quadratic Actions (F.G. Timmesfeld) -- Problem Set.- En línea: http://dx.doi.org/10.1007/978-1-4614-0709-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32743 Ejemplares
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Título : Categories and Sheaves Tipo de documento: documento electrónico Autores: Masaki Kashiwara ; SpringerLink (Online service) ; Schapira, Pierre Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, ISSN 0072-7830 num. 332 Número de páginas: X, 498 p Il.: online resource ISBN/ISSN/DL: 978-3-540-27950-1 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Manifolds Complex manifolds Theory, Algebra and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays. This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies Nota de contenido: The Language of Categories -- Limits -- Filtrant Limits -- Tensor Categories -- Generators and Representability -- Indization of Categories -- Localization -- Additive and Abelian Categories -- ?-accessible Objects and F-injective Objects -- Triangulated Categories -- Complexes in Additive Categories -- Complexes in Abelian Categories -- Derived Categories -- Unbounded Derived Categories -- Indization and Derivation of Abelian Categories -- Grothendieck Topologies -- Sheaves on Grothendieck Topologies -- Abelian Sheaves -- Stacks and Twisted Sheaves En línea: http://dx.doi.org/10.1007/3-540-27950-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34909 Categories and Sheaves [documento electrónico] / Masaki Kashiwara ; SpringerLink (Online service) ; Schapira, Pierre . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - X, 498 p : online resource. - (Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, ISSN 0072-7830; 332) .
ISBN : 978-3-540-27950-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Manifolds Complex manifolds Theory, Algebra and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays. This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies Nota de contenido: The Language of Categories -- Limits -- Filtrant Limits -- Tensor Categories -- Generators and Representability -- Indization of Categories -- Localization -- Additive and Abelian Categories -- ?-accessible Objects and F-injective Objects -- Triangulated Categories -- Complexes in Additive Categories -- Complexes in Abelian Categories -- Derived Categories -- Unbounded Derived Categories -- Indization and Derivation of Abelian Categories -- Grothendieck Topologies -- Sheaves on Grothendieck Topologies -- Abelian Sheaves -- Stacks and Twisted Sheaves En línea: http://dx.doi.org/10.1007/3-540-27950-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34909 Ejemplares
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Título : A Guide to the Classification Theorem for Compact Surfaces Tipo de documento: documento electrónico Autores: Jean Gallier ; SpringerLink (Online service) ; Dianna Xu Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Geometry and Computing, ISSN 1866-6795 num. 9 Número de páginas: XII, 178 p. 78 illus., 20 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-642-34364-3 Idioma : Inglés (eng) Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology Nota de contenido: The Classification Theorem: Informal Presentation -- Surfaces -- Simplices, Complexes, and Triangulations -- The Fundamental Group, Orientability -- Homology Groups -- The Classification Theorem for Compact Surfaces -- Viewing the Real Projective Plane in R3 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes En línea: http://dx.doi.org/10.1007/978-3-642-34364-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32549 A Guide to the Classification Theorem for Compact Surfaces [documento electrónico] / Jean Gallier ; SpringerLink (Online service) ; Dianna Xu . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XII, 178 p. 78 illus., 20 illus. in color : online resource. - (Geometry and Computing, ISSN 1866-6795; 9) .
ISBN : 978-3-642-34364-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology Nota de contenido: The Classification Theorem: Informal Presentation -- Surfaces -- Simplices, Complexes, and Triangulations -- The Fundamental Group, Orientability -- Homology Groups -- The Classification Theorem for Compact Surfaces -- Viewing the Real Projective Plane in R3 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes En línea: http://dx.doi.org/10.1007/978-3-642-34364-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32549 Ejemplares
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Título : Introduction to Topological Manifolds Tipo de documento: documento electrónico Autores: John M. Lee ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 202 Número de páginas: XVII, 433 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7940-7 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Topology Clasificación: 51 Matemáticas Resumen: This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness. This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book Nota de contenido: Preface -- 1 Introduction -- 2 Topological Spaces -- 3 New Spaces from Old -- 4 Connectedness and Compactness -- 5 Cell Complexes -- 6 Compact Surfaces -- 7 Homotopy and the Fundamental Group -- 8 The Circle -- 9 Some Group Theory -- 10 The Seifert-Van Kampen Theorem -- 11 Covering Maps -- 12 Group Actions and Covering Maps -- 13 Homology -- Appendix A: Review of Set Theory -- Appendix B: Review of Metric Spaces -- Appendix C: Review of Group Theory -- References -- Notation Index -- Subject Index En línea: http://dx.doi.org/10.1007/978-1-4419-7940-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33177 Introduction to Topological Manifolds [documento electrónico] / John M. Lee ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2011 . - XVII, 433 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 202) .
ISBN : 978-1-4419-7940-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Topology Clasificación: 51 Matemáticas Resumen: This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness. This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book Nota de contenido: Preface -- 1 Introduction -- 2 Topological Spaces -- 3 New Spaces from Old -- 4 Connectedness and Compactness -- 5 Cell Complexes -- 6 Compact Surfaces -- 7 Homotopy and the Fundamental Group -- 8 The Circle -- 9 Some Group Theory -- 10 The Seifert-Van Kampen Theorem -- 11 Covering Maps -- 12 Group Actions and Covering Maps -- 13 Homology -- Appendix A: Review of Set Theory -- Appendix B: Review of Metric Spaces -- Appendix C: Review of Group Theory -- References -- Notation Index -- Subject Index En línea: http://dx.doi.org/10.1007/978-1-4419-7940-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33177 Ejemplares
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Título : Simplicial Structures in Topology Tipo de documento: documento electrónico Autores: Davide L. Ferrario ; SpringerLink (Online service) ; Renzo A. Piccinini Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, ISSN 1613-5237 Número de páginas: XVI, 243 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7236-1 Idioma : Inglés (eng) Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in a short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henri Poincaré (singular homology is not discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful Nota de contenido: Preface -- Fundamental Concepts -- Simplicial Complexes -- Homology of Polyhedra -- Cohonology -- Triangulable Manifolds -- Homotopy Groups -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7236-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33156 Simplicial Structures in Topology [documento electrónico] / Davide L. Ferrario ; SpringerLink (Online service) ; Renzo A. Piccinini . - New York, NY : Springer New York : Imprint: Springer, 2011 . - XVI, 243 p : online resource. - (CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, ISSN 1613-5237) .
ISBN : 978-1-4419-7236-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in a short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henri Poincaré (singular homology is not discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful Nota de contenido: Preface -- Fundamental Concepts -- Simplicial Complexes -- Homology of Polyhedra -- Cohonology -- Triangulable Manifolds -- Homotopy Groups -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7236-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33156 Ejemplares
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