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https://math.stackexchange.com/questions/521265/understanding-cohomology-with-compact-support
Understanding cohomology with compact support. Ask Question Asked 6 years, 1 month ago. Active 6 years, 1 month ago. Viewed 3k times 6. 1 $\begingroup$ I am trying to understand the definition of (singular) cohomology with compact supports. My understanding of singular cohomology goes …
https://math.stackexchange.com/questions/770201/show-that-the-compactly-supported-de-rham-cohomology-groups-hp-dr-mathbb
Compactly supported cohomology is the cohomology of the complex of compactly supported differential forms (i.e., smooth forms that are zero outside of some compact set). Let's denote compactly supported cohomology and the usual de Rham cohomology by …
https://mathoverflow.net/questions/59017/group-cohomology-with-compact-support
I don't think there is a way to define cohomology with compact support in a purely group theoretic way. The problem is that compact cohomology will distinguish between multiple cusps, but cocycles can only capture one cusp. The result are modular symbols. answered Mar 30 '15 at 19:03
http://www.math.wisc.edu/~maxim/Topnotes9.pdf
1 Cohomolgy with Compact Support Let Xbe a topological space and Kbe a compact subset of X, ... is called the cohomology of Xwith compact support. De nition of Direct Limit of Groups (G ) 2I Let G be abelian groups indexed by some directed set I, namely, Iis partially ordered and
http://tungsteno.io/post/def-de_rham_cohomology_groups_compact_support/
But we have already seen that for the integration to be defined rigorously we have to stick to compact support differential forms. Surprisingly enough, this restriction leads to another type of cohomology. The restriction of the de Rham complex to compact support differential forms leads to a new complex
https://ncatlab.org/nlab/show/compactly+supported+cohomology
In compactly supported cohomology cocycles and coboundaries on some space are required to have compact support : to be non-trivial only over a compact subspace / compact subobject of the base.
https://www.physicsforums.com/threads/cohomology-with-compact-support.570117/
Jan 23, 2012 · So in singular cohomology with compact support, you consider the subcomplex of C^k(X) of those singular k-cochains f having the property (P) there exists a compact subset K of X such that f(c)= 0 for all k-chains c sitting outside of K.
http://tungsteno.io/post/exa-de_rham_cohomology_r_2_compact_support/
de Rham Cohomology of R² with Compact Support Tungsteno is a project whose goal is to make mathematics accessible to everybody, completely free, based on open collaboration and the best pedagogical tools Free, open-source online mathematics for students, teachers and workers
https://en.wikipedia.org/wiki/%C3%89tale_cohomology
The étale cohomology groups with compact support of a variety X are defined to be H c q ( X , F ) = H q ( Y , j ! F ) {\displaystyle H_{c}^{q}(X,F)=H^{q}(Y,j_{!}F)}
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