2024-02-25   28539

Homology Groups

Homology groups are examples of topological invariants: topologically equivalent spaces have the same homology groups. The idea behind homology groups is to consider a special family of topological spaces C for which the concept of a boundary makes sense, namely spaces made of simple polyhedra, and to use maps from those spaces into another topological space X as a way of exploring the topology of X. Roughly, the nth homology group of X describes continuous maps into X from those special n-dimensional spaces C that cannot be extended to a continuous map into X from any of the special (n+1)-dimensional spaces whose boundary is C.

Download PDF (25 pages, 316 KB)

Revision history


www.cphysics.org updated 2024-04-08