Introduction to topology and geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2013
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Cover image Inhaltsverzeichnis |
| Beschreibung: | "Presenting upper graduate level material in an accessible way for undergraduates, this Second Edition strikes a welcome balance between academic rigor and accessibility while covering an unparalleled range of topics, including the elements of projective geometry, conics and the applications and properties of conic selections, cross ratio points of infinity and fundamental transformations of projective geometry, the points of a homography/involution, and more. In addition, this comprehensive book includes numerous exercises and historical notes"-- Provided by publisher. Stahl, Saul: Introduction to topology and geometry Includes bibliographical references and index |
| Beschreibung: | XVI, 512 zahlr. graph. Darst. |
| ISBN: | 9781118108109 |
Internformat
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| 500 | |a Stahl, Saul: Introduction to topology and geometry | ||
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Geometry | |
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Datensatz im Suchindex
| _version_ | 1804150292855390208 |
|---|---|
| adam_text | Titel: Introduction to topology and geometry
Autor: Stahl, Saul
Jahr: 2013
CONTENTS
Preface xi
Acknowledgments xv
1 Informal Topology 1
2 Graphs 13
2.1 Nodes and Ares 13
2.2 Traversability 16
2.3 Colorings 21
2.4 Planarity 25
2.5 Graph Homeomorphisms 31
3 Surfaces 41
3.1 Polygonal Presentations 42
3.2 Closed Surfaces 50
3.3 Operations on Surfaces 71
3.4 Bordered Surfaces 79
3.5 Riemann Surfaces 94
vii
VIII CONTENTS
4 Graphs and Surfaces 103
4.1 Embeddings and Their Regions 103
4.2 Polygonal Embeddings 113
4.3 Embedding a Fixed Graph 118
4.4 Voltage Graphs and Their Coverings 128
Appendix 141
5 Knots and Links 143
5.1 Preliminaries 144
5.2 Labelings 147
5.3 From Graphs to Links and on to Surfaces 158
5.4 The Jones Polynomial 169
5.5 The Jones Polynomial and Alternating Diagrams 187
5.6 Knots and Surfaces 194
6 The Differential Geometry of Surfaces 205
6.1 Surfaces, Normals, and Tangent Planes 205
6.2 The Gaussian Curvature 212
6.3 The First Fundamental Form 219
6.4 Normal Curvatures 229
6.5 The Geodesic Polar Parametrization 236
6.6 Polyhedral Surfaces I 242
6.7 Gauss s Total Curvature Theorem 247
6.8 Polyhedral Surfaces II 252
7 Riemann Geometries 259
8 Hyperbolic Geometry 275
8.1 Neutral Geometry 275
8.2 The Upper Half-plane 287
8.3 The Half-Plane Theorem of Pythagoras 295
8.4 Half-Plane Isometries 305
9 The Fundamental Group 317
9.1 Definitions and the Punctured Plane 317
9.2 Surfaces 325
9.3 3-Manifolds 332
9.4 The Poincare Conjecture 357
CONTENTS IX
10 General Topology 361
10.1 Metrie and Topological Spaces 361
10.2 Continuity and Homeomorphisms 367
10.3 Connectedness 377
10.4 Compactness 379
11 Polytopes 387
11.1 Introduction to Polytopes 387
11.2 Graphs of Polytopes 400
11.3 Regulär Polytopes 404
11.4 Enumerating Faces 415
Appendix A Curves 429
A.l Parametrization of Curves and Arclength 429
Appendix B A Brief Survey of Groups 441
B.l The General Background 441
B.2 Abelian Groups 446
B.3 Group Presentations 447
Appendix C Permutations 457
Appendix D Modular Arithmetic 461
Appendix E Solutions and Hints to Selected Exercises 465
References and Resources 497
Index 505
|
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| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-10T00:36:37Z |
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| isbn | 9781118108109 |
| language | English |
| lccn | 2012040259 |
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| spelling | Stahl, Saul 1942- Verfasser (DE-588)1022190660 aut Introduction to topology and geometry Saul Stahl ; Catherine Stenson 2. ed. Hoboken, NJ Wiley 2013 XVI, 512 zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics "Presenting upper graduate level material in an accessible way for undergraduates, this Second Edition strikes a welcome balance between academic rigor and accessibility while covering an unparalleled range of topics, including the elements of projective geometry, conics and the applications and properties of conic selections, cross ratio points of infinity and fundamental transformations of projective geometry, the points of a homography/involution, and more. In addition, this comprehensive book includes numerous exercises and historical notes"-- Provided by publisher. Stahl, Saul: Introduction to topology and geometry Includes bibliographical references and index Topology Geometry MATHEMATICS / Topology bisacsh Geometrie (DE-588)4020236-7 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Geometrie (DE-588)4020236-7 s Stenson, Catherine 1972- Verfasser (DE-588)1035497182 aut http://catalogimages.wiley.com/images/db/jimages/9781118108109.jpg Cover image HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025954225&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stahl, Saul 1942- Stenson, Catherine 1972- Introduction to topology and geometry Topology Geometry MATHEMATICS / Topology bisacsh Geometrie (DE-588)4020236-7 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4060425-1 |
| title | Introduction to topology and geometry |
| title_auth | Introduction to topology and geometry |
| title_exact_search | Introduction to topology and geometry |
| title_full | Introduction to topology and geometry Saul Stahl ; Catherine Stenson |
| title_fullStr | Introduction to topology and geometry Saul Stahl ; Catherine Stenson |
| title_full_unstemmed | Introduction to topology and geometry Saul Stahl ; Catherine Stenson |
| title_short | Introduction to topology and geometry |
| title_sort | introduction to topology and geometry |
| topic | Topology Geometry MATHEMATICS / Topology bisacsh Geometrie (DE-588)4020236-7 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topology Geometry MATHEMATICS / Topology Geometrie Topologie |
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