All Questions
Tagged with at.algebraic-topology sheaf-theory
111 questions
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Spectral sequences in Hypercohomology of sheaves
Alright, here I go again, don't know if I'm missing something here but let $X$ be a topological space and let $F^{\bullet}$ be a cochain complex of sheaves, I want to compute the cohomology of this ...
- 23k
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Hypercohomology of a complex of sheaves that might be acyclic (or might not)
Back again, check this out, let $X$ be a topological space and let $F^{\bullet}$ be a cochain complex of sheaves, I'm trying to compute the cohomology of the complex of global sections of the sheaves
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- 42.9k
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Where can I find a proof of the de Rham-Weil theorem?
Where can I find a proof of the de Rham-Weil theorem?
Does anyone know?
- 34.7k
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Orientation Sheaf and Double Cover
The orientation sheaf of an $n$-manifold $M$ is $\mathcal{O}_n=Sheaf(U\mapsto H_n(M,M-U;\mathbb{Z}))$, with stalks given by $(\mathcal{O}_n)_x = lim H_n(M,M-U)=H_n(M,M-x)=\mathbb{Z}$ (the limit is ...
- 44.4k
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Derived Equivalence of Sheaves and Homotopy
This question loosely elaborates on an earlier question. It is pretty silly, but I'd like to hear some authoritative answers.
Recall that if $f:S^{\bullet}\to T^{\bullet}$ is a quasi-isomorphism of ...
CommunityBot
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Does one need to sheafify when defining the inverse image of a sheaf with respect to an embedding?
This seems to be a rather simple (stupid?:)) question; yet I was not able to find an answer quickly.
For a morphism $f:X\to Y$ of schemes (or topological spaces) and an (etale or topological) sheaf $...
- 721
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Exercise concerning locally constant presheaves [closed]
Let $\mathscr{F}$ be a presheaf of abelian groups on some topological space $X$. We say that $\mathscr{F}$ is locally constant if there exists an open cover $\mathcal{U}$ of $X$ (i.e. $X=\bigcup_{U\in\...
- 4,902
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Dualizing complex of the product of two locally compact spaces
Hello!
In the setting of locally compact Hausdorff spaces, I would like to understand the relation between the exterior product ${\mathbb D}_X\boxtimes{\mathbb D}_Y$ of the dualizing complexes of two ...
- 2,756
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Applications of sheaf theory to the computation of invariants of LS-category type
I would like to know if sheaf theory can be applied to a particular class of questions in topology.
The Schwarz genus (also known as sectional category) of a continuous map $p\colon\thinspace E\to ...
- 35.9k
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Why is this a local constant sheaf
If a group $G$ acts on a topological space $M$, and a representation of $G$ on a vector space $V$, why $M \times_G V$ is a local constant sheaf over $M/G$?
- 57.6k
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Descent of singular cohomology
When proving that singular cohomology of an appropriate space $X$ equals sheaf cohomology of $X$ with "values" (does one say that?) in the sheaf $\mathbb{Z}_X$ of locally constant functions, the ...
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