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Results tagged with at.algebraic-topology
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user 107013
Homotopy theory, homological algebra, algebraic treatments of manifolds.
6
votes
1
answer
823
views
De Rham's theorem for top-forms in manifolds with boundary
In page 79 of Bott-Tu, "Differential Forms in Algebraic Topology", they define the relative de Rham theory as follows:
Let $f:S\to M$ be a smooth map. Define the complex $\Omega^*(f)$ by
$$\Omega^k(f) …
- 101
4
votes
Accepted
De Rham's theorem for top-forms in manifolds with boundary
It is indeed true that $H^n(M)=0$ if $M$ is a compact manifold with boundary. In particular, $H^n(M,\partial M)\cong\mathbb{R}$ by Lefschetz duality (as Chris Gerig mentioned) and the integral (1) is …
- 101