Transcription of Preface - pi.math.cornell.edu
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Preface - pi.math.cornell.edu
Preface .. ixStandard Notations 0. Some Underlying Geometric Notions.. 1 Homotopy and Homotopy Type 1. Cell Complexes on Spaces 8. Two Criteria for Homotopy Equivalence Homotopy Extension Property 1. The Fundamental Group.. Basic Constructions.. 25 Paths and Homotopy 25. The Fundamental Group of the Circle Homomorphisms Van Kampen s Theorem.. 40 Free Products of Groups 41. The van Kampen Theorem to Cell Complexes Covering Spaces.. 56 Lifting Properties 60. The Classification of Covering Spaces Transformations and Group Actions Graphs and Free Groups K(G,1) Spaces and Graphs of Groups 2. Homology.. Simplicial and Singular Homology.. 102 Complexes 102. Simplicial Homology 104. Singular Invariance 110. Exact Sequences and Excision Equivalence of Simplicial and Singular Homology Computations and Applications.. 134 Degree 134. Cellular Homology 137. Mayer-Vietoris Sequences with Coefficients The Formal Viewpoint.
Preface xi Eilenberg and Zilber in 1950 under the name of semisimplicial complexes. Soon after this, additional structure in the form of certain ‘degeneracy maps’ was introduced,
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