Homology Groups

Abstract

The homotopy groups πn(X, x0) of a space are relatively easy to define, clearly topological invariants and, indeed, invariants of homotopy type, but are also extraordinarily difficult to compute even for quite simple spaces. Now we intend to provide a brief introduction to another set of invariants for which this situation is reversed. The singular homology groups require some work to define and their homotopy invariance is not so obvious, but once some basic tools are developed their computation is comparatively straightforward.KeywordsChain ComplexHomology GroupShort Exact SequenceHomology ClassFree Abelian GroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.