代数拓扑导论
2009-8
世界图书出版公司
罗曼
433
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There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to .I.H.C. Whitehead. Of course, this is false, as a giance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details.Tbere are two types of obstacle for the student learning algebraic topology. The first is the formidable array of new techniques （e.g., most students know very little homological algebra）; the second obstacle is that the basic definitions have been so abstracted that their geometric or analytic origins have been obscured. I have tried to overcome these barriers. In the first instance, new definitions are introduced only when needed （e.g., homology with coefficents and cohomology are deferred until after the EilenbergSteenrod axioms have been verified for the three homology theories we treat——singular, simplicial, and cellular）. Moreover, many exercises are given to help the reader assimilate material. In the second instance, important definitions are often accompanied by an informal discussion describing their origins （e.g., winding numbers are discussed before computing, Green's theorem occurs before defining homology, and differential forms appear before introducing cohomology）.
There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to .I.H.C. Whitehead. Of course， this is false， as a giance at the books of Hilton and Wylie， Maunder， Munkres， and Schubert reveals. Still， the canard does reflect some truth. Too often one finds too much generality and too little attention to details.
作者：(美国)罗曼
PrefaceTo the ReaderCHAPTER 0 Introduction Notation Brouwer Fixed Point Theorem Categories and FunctorsCHAPTER 1 Some Basic Topological Notions Homotopy Convexity, Contractibility, and Cones Paths and Path ConnectednessCHAPTER 2 Simplexes Affine Spaces Aftine MapsCHAPTER 3 The Fundamental Group The Fundamental Groupoid The Functor π π1(S1)CHAPTER 4 Singular Homology Holes and Green's Theorem Free Abelian Groups The Singular Complex and Homology Functors Dimension Axiom and Compact Supports The Homotopy Axiom The Hurewicz TheoremCHAPTER 5 Long Exact Sequences The Category Comp Exact Homology Sequences Reduced HomologyCHAPTER 6 Excision and Applications Excision and Mayer-Vietoris Homology of Spheres and Some Applications Barycentric Subdivision and the Proof of Excision Moxe Applications to Euclidean SpaceCHAPTER 7 Simplicial Complexes Definitions Simplicial Approximation Abstract Simplicial Complexes Simplicial Homology Comparison with Singular Homology Calculations Fundamental Groups of Polyhedra The Seifert-van Kampen TheoremCHAPTER 8 CW Complexes Hausdorff Quotient Spaces Attaching Calls Homology and Attaching Cells CW Complexes Cellular HomologyCHAPTER 9 Natural Transformations Definitions and Examples Eilenberg-Steenrod Axioms ……CHAPTER 10 Covering SpacesCHAPTER 11 Homotopy GroupsCHPATER 12 CohomologyBibliographyNotationIndex
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《代数拓扑导论(英文版)》是由世界图书出版公司出版。
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写得不错的
代数拓扑是当今数学研究的主流，希望通过这门课程学习能提高代数拓扑的修养！
rotman是spanier的学生，他是研究代数学的，这本书多少有点spanier那本经典著作的影子，当然难度自然是降低了不少，写的很友好。
质量挺好，快递送货及时