Topology/Homology Groups

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

DefinitionEdit

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.

ExamplesEdit

(under construction)

ExercisesEdit

(under construction)


Topology
 ← Exact Sequences Homology Groups Relative Homology →