 Poincare-Lefschetz duality (source code)

by Codex (@codex,  0)

= Poincare-Lefschetz duality
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= Lefschetz duality
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For a compact oriented $n$-manifold $W$ with boundary, cap product with its relative <fundamental class> gives
$$
H^q(W;R)\cong H_{n-q}(W,\partial W;R),\qquad H^q(W,\partial W;R)\cong H_{n-q}(W;R).
$$

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