Ebook: Mod Two Homology and Cohomology

Intro; Contents; 1 Introduction; 2 Simplicial (Co)homology; 2.1 Simplicial Complexes; 2.2 Definitions of Simplicial (Co)homology; 2.3 Kronecker Pairs; 2.4 First Computations; 2.4.1 Reduction to Components; 2.4.2 0-Dimensional (Co)homology; 2.4.3 Pseudomanifolds; 2.4.4 Poincaré Series and Polynomials; 2.4.5 (Co)homology of a Cone; 2.4.6 The Euler Characteristic; 2.4.7 Surfaces; 2.5 The Homomorphism Induced by a Simplicial Map; 2.6 Exact Sequences; 2.7 Relative (Co)homology; 2.8 Mayer-Vietoris Sequences; 2.9 Appendix A: An Acyclic Carrier Result; 2.10 Appendix B: Ordered Simplicial (Co)homology