Author | Croom, Fred H. author |
---|---|
Title | Basic Concepts of Algebraic Topology [electronic resource] / by Fred H. Croom |
Imprint | New York, NY : Springer New York, 1978 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9475-4 |
Descript | X, 180 p. online resource |
1 Geometric Complexes and Polyhedra -- 1.1 Introduction -- 1.2 Examples -- 1.3 Geometric Complexes and Polyhedra -- 1.4 Orientation of Geometric Complexes -- 2 Simplicial Homology Groups -- 2.1 Chains, Cycles, Boundaries, and Homology Groups -- 2.2 Examples of Homology Groups -- 2.3 The Structure of Homology Groups -- 2.4 The Euler-Poincarรฉ Theorem -- 2.5 Pseudomanifolds and the Homology Groups of Sn -- 3 Simplicial Approximation -- 3.1 Introduction -- 3.2 Simplicial Approximation -- 3.3 Induced Homomorphisms on the Homology Groups -- 3.4 The Brouwer Fixed Point Theorem and Related Results -- 4 The Fundamental Group -- 4.1 Introduction -- 4.2 Homotopic Paths and the Fundamental Group -- 4.3 The Covering Homotopy Property for S1 -- 4.4 Examples of Fundamental Groups -- 4.5 The Relation Between H1(K) and ?1( |) -- 5 Covering Spaces -- 5.1 The Definition and Some Examples -- 5.2 Basic Properties of Covering Spaces -- 5.3 Classification of Covering Spaces -- 5.4 Universal Covering Spaces -- 5.5 Applications -- 6 The Higher Homotopy Groups -- 6.1 Introduction -- 6.2 Equivalent Definitions of ?n(X, x0) -- 6.3 Basic Properties and Examples -- 6.4 Homotopy Equivalence -- 6.5 Homotopy Groups of Spheres -- 6.6 The Relation Between Hn(K) and ?n( |) -- 7 Further Developments in Homology -- 7.1 Chain Derivation -- 7.2 The Lefschetz Fixed Point Theorem -- 7.3 Relative Homology Groups -- 7.4 Singular Homology Theory -- 7.5 Axioms for Homology Theory -- Appendix 1. Set Theory -- Appendix 2. Point-set Topology -- Appendix 3. Algebra