List questions from sheaf-theory

Published on 15 Jul 2014 - 17:17

222

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Principal Bundle- Definition cum Exercise from "Geometry and Topology" by Bredon

Published on 25 Mar 2026 - 14:22

104

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$i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism.

Published on 16 Jul 2014 - 15:12

34

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$i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism

Published on 16 Jul 2014 - 15:22

64

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Well-definedness of the action of the structure group of a principal bundle on the total space.

Published on 25 Mar 2026 - 12:50

100

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Why $F \leq F' \; \Leftarrow \; \forall x \in X \; F_x \subseteq F'_x$?

Published on 18 Jul 2014 - 7:10

466

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Group of Automorphism of the Fiber of Fiber Bundle

Published on 26 Mar 2026 - 7:35

321

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Asterisk Notation

Published on 25 Mar 2026 - 22:25

472

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When are two morphisms of sheaves the same?

Published on 22 Jul 2014 - 20:23

166

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Only $f^\sharp_x$ makes the diagram commutative

Published on 23 Jul 2014 - 17:10

129

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Question on the definition of sheaves.

Published on 25 Mar 2026 - 16:02

510

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Connection between differential form of a manifold and Sheaf of relative differential of a map of schemes.

Published on 25 Jul 2014 - 3:25

453

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Is this sequence of presheaves exact?

Published on 25 Jul 2014 - 9:38

272

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Cohomology Calculation

Published on 25 Jul 2014 - 11:10

210

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Prove that $H^1(\mathcal{M}^*)=0$.

Published on 25 Mar 2026 - 22:23

List Question

$f^+\mathscr{G}$ not a sheaf even if $\mathscr{G}$ is

Principal Bundle- Definition cum Exercise from "Geometry and Topology" by Bredon

$i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism.

$i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism

Well-definedness of the action of the structure group of a principal bundle on the total space.

Why $F \leq F' \; \Leftarrow \; \forall x \in X \; F_x \subseteq F'_x$?

Group of Automorphism of the Fiber of Fiber Bundle

Asterisk Notation

When are two morphisms of sheaves the same?

Only $f^\sharp_x$ makes the diagram commutative

Question on the definition of sheaves.

Connection between differential form of a manifold and Sheaf of relative differential of a map of schemes.

Is this sequence of presheaves exact?

Cohomology Calculation

Prove that $H^1(\mathcal{M}^*)=0$.

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