Author | Fulton, William. author |
---|---|
Title | Algebraic Topology [electronic resource] : A First Course / by William Fulton |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4180-5 |
Descript | XVIII, 430 p. 13 illus. online resource |
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 MayerโVietoris -- 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 RiemannโRoch 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; Gaussโs 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 Borsukโs Theorem -- Hints and Answers -- References -- Index of Symbols