http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
1 online resource (xviii, 430 pages) : illustrations.
This book introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. Rather than choosing one point of view of modern topology (homotropy theory, axiomatic homology, or differential topology, say) the author concentrates on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts; it is also in harmony with the historical development of the subject. The book is aimed at students who do not necessarily intend on specializing in algebraic topology.
Ch. 1. Path Integrals -- Ch. 2. Angles and Deformations -- Ch. 3. The Winding Number -- Ch. 4. Applications of Winding Numbers -- Ch. 5. De Rham Cohomology and the Jordan Curve Theorem -- Ch. 6. Homology -- Ch. 7. Indices of Vector Fields -- Ch. 8. Vector Fields on Surfaces -- Ch. 9. Holes and Integrals -- Ch. 10. Mayer-Vietoris -- Ch. 11. Covering Spaces -- Ch. 12. The Fundamental Group -- Ch. 13. The Fundamental Group and Covering Spaces -- Ch. 14. The Van Kampen Theorem -- Ch. 15. Cohomology -- Ch. 16. Variations -- Ch. 17. The Topology of Surfaces -- Ch. 18. Cohomology on Surfaces -- Ch. 19. Riemann Surfaces -- Ch. 20. Riemann Surfaces and Algebraic Curves -- Ch. 21. The Riemann-Roch Theorem -- Ch. 22. Toward Higher Dimensions -- Ch. 23. Higher Homology -- Ch. 24. Duality -- Appendix A: Point Set Topology -- Appendix B: Analysis -- Appendix C: Algebra -- Appendix D: On Surfaces -- Appendix E: Proof of Borsuk's Theorem.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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Includes bibliographical references (pages 419-420) and indexes.
0387943269 (New York : hardcover : acid-free paper)
9780387943268 (New York : hardcover : acid-free paper)
0387943277 (New York : softcover : acid-free paper)
9780387943275 (New York : softcover : acid-free paper)
3540943269 (Berlin : hardcover : acid-free paper)
9783540943266 (Berlin : hardcover : acid-free paper)
3540943277 (Berlin : softcover : acid-free paper)
9783540943273 (Berlin : softcover : acid-free paper)