作者：（美）罗曼著
页数：433
出版社：世界图书出版公司
出版日期：2009
ISBN：9787506282802
电子书格式：pdf/epub/txt
内容简介
《代数拓扑导论(英文版)》介绍了：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.
本书特色
Doing exercises is an essential part of learning mathematics, and the serious reader of this book should attempt to solve all the exercises as they arise. An asterisk indicates only that an exercise is cited elsewhere in the text, sometimes in a proof (those exercises used in proofs, however, are always routine).
目录
to the reader
chapter 0 introduction
notation
brouwer fixed point theorem
categories and functors
chapter 1 some basic topological notions
homotopy
convexity, contractibility, and cones
paths and path connectedness
chapter 2 simplexes
affine spaces
aftine maps
chapter 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 theorem
chapter 5 long exact sequences
the category comp
exact homology sequences
reduced homology
chapter 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 space
chapter 7 simplicial complexes
definitions
simplicial approximation
abstract simplicial complexes
simplicial homology
comparison with singular homology
calculations
fundamental groups of polyhedra
the seifert-van kampen theorem
chapter 8 cw complexes
hausdorff quotient spaces
attaching calls
homology and attaching cells
cw complexes
cellular homology
chapter 9 natural transformations
definitions and examples
eilenberg-steenrod axioms
……
chapter 10 covering spaces
chapter 11 homotopy groups
chpater 12 cohomology
bibliography
notation
index
