Topology/Homology Groups

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

Definition
Given a chain complex


 * $$\cdots\xrightarrow{\partial_2}C_2\xrightarrow{\partial_1}C_1\xrightarrow{\partial_0}C_0$$

the n-th homology group is


 * $$H_n=Ker(\partial_n)/Im(\partial_{n+1})$$. We have a similar situation to the fundamental group.

Examples
(under construction)

Exercises
(under construction)