Definition
Given a subspace, one may form the short exact sequence
where denotes the singular chains on the space X. The boundary map on leaves invariant and therefore descends to a boundary map on the quotient. The corresponding homology is called relative homology:
One says that relative homology is given by the relative cycles, chains whose boundaries are chains on A, modulo the relative boundaries (chains that are homologous to a chain on A, i.e. chains that would be boundaries, modulo A again).
Read more about this topic: Relative Homology
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