reconcile two different cohomolgies

I remain in the procedure of persuading myself of particular outcomes:

I see that in the portable assistance cohomology mayer vietoris has actually contrary rows contrasted to the one in single geography nonetheless it is claimed that those 2 cohomologies coincide in instance the room is claim a compact shut linked manifold. Just how is that?

I recognize I am really overwhelmed I wish I am not perplexing you either ;)

Thank you beforehand

1
2022-06-07 14:31:41
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Answers: 1

Let me do it with de Rham cohomology, for selection:

One specifies the de Rham cohomology $H^\bullet(M)$ of a manifold $M$ beginning with differential kinds on $M$, and also one specifies the compactly sustained de Rham cohomology $H_c^\bullet(M)$ of a manifold $M$ beginning with differential kinds on $M$ which have portable assistance .

Currently, if $M$ is a portable manifold, every differential kind on $M$ has portable assistance (due to the fact that the assistance of something is a shut part of $M$, which is instantly portable in this instance) so in this instance the credentials "with portable suppot" does not, actually, exclude any kind of kind. It adheres to quickly that $H^\bullet(M)$ and also $H^\bullet_c(M)$ synchronize.

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2022-06-07 14:49:46
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