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Results tagged with derham-cohomology
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user 118688
Better spelling "DeRham", not derham... I can't figure out how to change this... moderators? The cohomology of the complex of differential forms on a smooth manifold with differential given by exterior derivative.
6
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3
answers
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Classification of line bundles by second cohomology of a manifold
In the book Loop spaces, Characteristic classes and geometric quantization by Brylinski I see following result when trying to motivate geometric description of $H^3(M,\mathbb{Z})$.
$H^2(M,\mathbb{ …
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6
votes
1
answer
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De Rham cohomology of Lie groupoid
Let $G$ be a Lie group acting on a manifold $M$.
Consider the transformation groupoid $\mathcal{G}=(G\times M\rightrightarrows M)$. We have the notion of de Rham cohomology of a Lie groupoid by con …
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6
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0
answers
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Geometric theory for cohomology groups $H^p(M;\mathbb{Z})$
An excerpt from the book Loop Spaces, Characteristic Classes and Geometric Quantization by Jean-Luc Brylinski is mentioned below:
Characteristic classes are certain cohomology classes associated
…
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3
votes
1
answer
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Models for computing cohomology of Lie groupoids
Given a Lie groupoid $\mathcal{G}=[\mathcal{G}_1\rightrightarrows \mathcal{G}_0]$, let $\mathcal{G}_\bullet$ be the associated simplicial manifold.
Let $\Omega^\bullet(\mathcal{G}_\bullet)$ be the a …
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1
vote
Accepted
De Rham cohomology of Lie groupoid
Proposition $13$ and Remark $16$ in page $10$ of Cohomology or Stacks says that, there is a natural isomorphism
$$H^i_G(X)\rightarrow H^i(X\times G\rightrightarrows X)$$
where, $H^i_G(X)$ is the $i^ …
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2
votes
1
answer
358
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Easier ways to compute homology/cohomology by adding extra structure
Suppose $X$ is a topological space and I want to talk about its “homology”.
There is this notion of singular homology obtained from singular chain complex. This is not very easy to compute.
Suppose …
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3
votes
1
answer
573
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How does one introduce characteristic classes [closed]
How does one introduce, or how were you introduced to characteristic classes?
You can assume that the student is comfortable with principal bundles and connections on principal bundles.
I am not as …
2
votes
1
answer
821
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Sheaf / de Rham cohomology of a stack with values in a complex of abelian sheaves
I am reading Differentiable Stacks and Gerbes to understand about (hyper) cohomology groups of a stack $\mathcal{X}$ with values in a complex $\mathcal{M}$ of abelian sheaves over $\mathcal{X}$.
Reca …
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