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Algebraic Topology A First Course

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re­ lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular t...

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Bibliographic Details
Main Author: Fulton, William
Format: eBook
Language:English
Published: New York, NY Springer New York 1995, 1995
Edition:1st ed. 1995
Series:Graduate Texts in Mathematics
Subjects:
Topology
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I Calculus in the Plane
  • 1 Path Integrals
  • 2 Angles and Deformations
  • II Winding Numbers
  • 3 The Winding Number
  • 4 Applications of Winding Numbers
  • III Cohomology and Homology, I
  • 5 De Rham Cohomology and the Jordan Curve Theorem
  • 6 Homology
  • IV Vector Fields
  • 7 Indices of Vector Fields
  • 8 Vector Fields on Surfaces
  • V Cohomology and Homology, II
  • 9 Holes and Integrals
  • 10 Mayer—Vietoris
  • VI Covering Spaces and Fundamental Groups, I
  • 11 Covering Spaces
  • 12 The Fundamental Group
  • VII Covering Spaces and Fundamental Groups, II
  • 13 The Fundamental Group and Covering Spaces
  • 14 The Van Kampen Theorem
  • VIII Cohomology and Homology, III
  • 15 Cohomology
  • 16 Variations
  • IX Topology of Surfaces
  • 17 The Topology of Surfaces
  • 18 Cohomology on Surfaces
  • X Riemann Surfaces
  • 19 Riemann Surfaces
  • 20 Riemann Surfaces and Algebraic Curves
  • 21 The Riemann—Roch Theorem
  • XI Higher Dimensions
  • 22 Toward Higher Dimensions
  • 23 Higher Homology
  • 24 Duality
  • Appendices
  • Appendix A Point Set Topology
  • A1. Some Basic Notions in Topology
  • A2. Connected Components
  • A3. Patching
  • A4. Lebesgue Lemma
  • Appendix B Analysis
  • B1. Results from Plane Calculus
  • B2. Partition of Unity
  • Appendix C Algebra
  • C1. Linear Algebra
  • C2. Groups; Free Abelian Groups
  • C3. Polynomials; Gauss’s Lemma
  • Appendix D On Surfaces
  • D1. Vector Fields on Plane Domains
  • D2. Charts and Vector Fields
  • D3. Differential Forms on a Surface
  • Appendix E Proof of Borsuk’s Theorem
  • Hints and Answers
  • References
  • Index of Symbols

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