For a pair A⊆X, the short exact sequence of chain complexes 0→C∗(A)→C∗(X)→C∗(X,A)→0 induces
⋯→Hn(A)→Hn(X)→Hn(X,A)∂Hn−1(A)→⋯.
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- Relative homology
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- Collapsing a simple closed curve on a surface
- Gysin sequence of an embedding
- Half-lives-half-dies theorem
- Homology after collapsing a nonseparating surface curve
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