All Questions
Tagged with sheaf-theory smooth-manifolds
7 questions with no upvoted or accepted answers
17
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Is there an Infinite dimensional sheaf theory for analysis on manifolds?
I apologize if this question is slightly vague but I don't know how to ask it non-vaguely. Moreover, my question is about an ideal situation. If there's a close answer which doesn't satisfy all the ...
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10
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Differential Forms in Infinite Dimensions
In Kriegl/Michor's book "The convenient setting of global analysis", they define the space of differential $k$-forms on a possibly infinite-dimensional manifold $M$ as the space of smooth sections of ...
- 9,853
5
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Sheaf-like reconstruction of a continuous function
Let $X$ and $Y$ be topological manifolds and let $\{(\phi_x,U_x)\}_{x \in X}$ and $\{(\psi_y,Y_y)\}_{y \in Y}$ be respective atlases of $X$ and $Y$; with each $\phi_x:U_x\rightarrow \mathbb{R}^n,\...
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4
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Question on de Rham complex with distributional coefficients
Let $X$ be a smooth manifold (usually assumed to be paracompact). Let us denote by $\underline{\Omega}^{p,-\infty}_X$ the sheaf of real valued $p$-forms with distributional coefficients in the ...
- 21.8k
2
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Pullback by surjective submersion is injective?
Denote by $\mathcal{D}'_X$ the sheaf of distributions on a smooth manifold $X$.
Let $M$ and $N$ be smooth manifolds and $\Phi: M \to N$ a submersion. Then $\Phi$ defines a unique morphism of sheaves $\...
- 261
2
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66
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For which locally ringed spaces is the structure sheaf given by LRS morphisms to the real line?
Let $\mathsf{LRS}_{\mathbb R}$ denote the category of locally $\mathbb R$-ringed spaces.
Given a locally ringed space $(X,\mathcal O_X)$, write $C_{(X,\mathcal O_X)}^p$ for the hom-sheaf on $X$ of ...
- 10.5k
1
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Proving that two given functionally structured spaces are isomorphic
The relevant definitions are listed below. They can be found in Chapter VI, pages 297-298 of Bredon's Introduction to Compact Transformation Groups; and Section 2, Chapter II of Bredon's Topology and ...
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