chapter  13
5 Pages

Relative Homology

WithMarvin J. Greenberg, John R. Harper

Let A be a subspace of X Then for every q ≥ 0, Sq (A) is the submodule of Sq (X) consisting of linear combinations of singular q-simplexes Δ q → X which actually map into A. We can then form the quotient module, and since the boundary operator sends Sq (A) into S q–1(A), it induces a homomorphism ∂ ¯ which makes the diagram