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Relative homology

Relative chain complex

{title2=$C_\bullet(K,L)$}

If $L$ is a <simplicial subcomplex> of $K$, then
$$
C_k(K,L)=C_k(K)/C_k(L).
$$
Its homology is the simplicial <relative homology> $H_k(K,L)$.

Relative simplicial chain complex

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 20F / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 20F / d / Solution

Relative homology of a simplex and its boundary

Relative simplicial chain complex ( $C_{∙} (K, L)$ )

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Relative simplicial chain complex (C∙​(K,L))

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Relative simplicial chain complex ( $C_{∙} (K, L)$ )

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