Algebraic Topology Winter Term 2014/15

Description

Basic definitions......Page 5 Basic constructions and examples......Page 9 Pullbacks and pushouts, attaching and CW-complexes......Page 14 Topological groups and homogeneous spaces......Page 24 Exercises for Chapter 1......Page 27 Categories and functors......Page 30 Modules......Page 42 Homological algebra......Page 52 Exercises for Chapter 2......Page 62 Homotopies and homotopy equivalences......Page 65 Fundamental group(oid)s......Page 70 The fundamental group of the circle......Page 80 The theorem of Seifert and van Kampen......Page 86 Supplement*: paths, homotopies and fundamental groupoids from the higher category perspective......Page 105 Exercises for Chapter 3......Page 117 Singular simplexes and -complexes......Page 123 Subspaces and relative homology......Page 136 Excision......Page 140 Exercises for Chapter 4......Page 150 The axiomatic formulation......Page 153 The mapping degree......Page 157 Homologies of CW-complexes......Page 162 Homology with coefficients......Page 170 Exercises for Section 5......Page 180