# Topology/Homology Groups

< Topology

A *homology group* is a group derived from a space's chain complex.

## Definition edit

Given a chain complex

the n-th homology group is

- . We have a similar situation to the fundamental group.

- Theorem

A continuous function on topological spaces always induces homomorphisms . If is a homeomorphism, is an isomorphism.

## Examples edit

(under construction)

## Exercises edit

(under construction)