Topology/Homology Groups

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

Definition

Given a chain complex

$\cdots \stackrel{{\partial }_2}{\to }{C}_2\stackrel{{\partial }_1}{\to }{C}_1\stackrel{{\partial }_0}{\to }{C}_0$

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)

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