List questions from algebraic-topology

Published on 12 Apr 2026 - 10:15

433

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Chern-Weil: why do we divide by $2\pi$?

Published on 25 Mar 2026 - 20:52

53

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Define $F:S^2\longrightarrow \mathbb R$ continuous such that $F|_{H_+}=f$ and $F|_{H_-}=g$?

Published on 15 Apr 2026 - 3:27

36

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Show $f$~$g$ iff $\overline {f}$~$\overline{g}$

Published on 17 Apr 2026 - 14:45

419

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Alexander duality formulation + Jordan-Brouwer separation

Published on 14 Apr 2026 - 12:58

1.1k

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Is every compact space compactly generated?

Published on 10 Apr 2026 - 10:00

135

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What is the $H_1(X)$ where $X$ is the boundary of the unit square and the vertical lines with rational first coordinate?

Published on 14 Apr 2026 - 7:05

4.3k

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Tangent bundle of P^n and Euler exact sequence

Published on 16 Apr 2026 - 4:34

2.3k

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Showing that every map $f : S^2 \rightarrow S^1$ is homotopic to the trivial map

Published on 15 Apr 2026 - 23:05

76

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Isomorphism of the etale fundamental group

Published on 14 Apr 2026 - 12:22

269

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$H$ a discrete subgroup of topological group $G$ $\implies$ there exists an open $U\supseteq\{1\}$ s.t. the $hU$ are pairwise disjoint

Published on 15 Apr 2026 - 8:47

77

Views

Prove that $h$ and $p*q$ are homotopic relative to {$0,1$}

Published on 14 Apr 2026 - 15:24

208

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Prove that if $f:D^2\to D^2$ is a homeomorphism, then $f(S^1)=S^1$

Published on 14 Apr 2026 - 19:38

579

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Describe all the quotient groups of $\mathbb{Z} \oplus \mathbb{Z}$

Published on 11 Apr 2026 - 23:50

761

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Examples of de Rham cohomology being easier to compute that singular cohomology

Published on 15 Apr 2026 - 12:59

List Question

Definition of a lift in algebraic topology

Chern-Weil: why do we divide by $2\pi$?

Define $F:S^2\longrightarrow \mathbb R$ continuous such that $F|_{H_+}=f$ and $F|_{H_-}=g$?

Show $f$~$g$ iff $\overline {f}$~$\overline{g}$

Alexander duality formulation + Jordan-Brouwer separation

Is every compact space compactly generated?

What is the $H_1(X)$ where $X$ is the boundary of the unit square and the vertical lines with rational first coordinate?

Tangent bundle of P^n and Euler exact sequence

Showing that every map $f : S^2 \rightarrow S^1$ is homotopic to the trivial map

Isomorphism of the etale fundamental group

$H$ a discrete subgroup of topological group $G$ $\implies$ there exists an open $U\supseteq\{1\}$ s.t. the $hU$ are pairwise disjoint

Prove that $h$ and $p*q$ are homotopic relative to {$0,1$}

Prove that if $f:D^2\to D^2$ is a homeomorphism, then $f(S^1)=S^1$

Describe all the quotient groups of $\mathbb{Z} \oplus \mathbb{Z}$

Examples of de Rham cohomology being easier to compute that singular cohomology

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