reduced homology

Overview

Reduced homology is a modification of singular homology so that the homology of a single point is always , this makes some statements a little clearer and generalized axioms for homology to fit better.

Definition

For a topological space and , then the reduced homology of is

where denotes the relative singular homology.

Note that for all then the reduced homology is the same as the usual homology. It can differ on .