List questions from algebraic-topology

Published on 15 Apr 2026 - 11:58

44

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Is this homology sequence right?

Published on 11 Apr 2026 - 6:34

321

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Do all homology 3-spheres bound some contractible 4-manifold

Published on 16 Apr 2026 - 0:05

278

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General questions about covering spaces

Published on 09 Apr 2026 - 0:04

124

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Proof that $f$ is not a homotopy equivalence

Published on 13 Apr 2026 - 2:18

229

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Show that any continuous map $f: S^2 \rightarrow KB$ is null-homotopic.

Published on 15 Apr 2026 - 17:37

82

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Let $f,g:\Delta_1\to X$ be two paths in $X$ such that $f(e_1)=g(e_0)$. Prove that $f*g-f-g\in S_1(x)$ is a 1-boundary.

Published on 16 Apr 2026 - 15:21

119

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$z_0^m+z_1^m+z_2^m+z_3^m=0$ defines a surface in $P^3$. What argument is used to compute euler characteristic?

Published on 16 Apr 2026 - 10:19

65

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$f$ is a cycle since it is a loop, and since $H_1(point) = 0$, $f$ must then be a boundary.

Published on 16 Apr 2026 - 4:22

480

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Could someone explain to me what a Teichmuller Space is?

Published on 09 Apr 2026 - 6:06

885

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Errata for Bott Tu Differential Forms

Published on 17 Apr 2026 - 4:33

941

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Different definitions of (co)homology with local coefficients

Published on 09 Apr 2026 - 2:05

280

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Serre fibrations have HLP against all CW complexes

Published on 16 Apr 2026 - 19:07

110

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Crossing Number of $K_5$ on the Tubular Neighborhood of a Trefoil Knot

Published on 30 Mar 2026 - 19:19

60

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Can two Lie groups be "almost" homeomorphic?

Published on 14 Apr 2026 - 12:16

List Question

2-cohomology group of complex compact algebraic surface

Is this homology sequence right?

Do all homology 3-spheres bound some contractible 4-manifold

General questions about covering spaces

Proof that $f$ is not a homotopy equivalence

Show that any continuous map $f: S^2 \rightarrow KB$ is null-homotopic.

Let $f,g:\Delta_1\to X$ be two paths in $X$ such that $f(e_1)=g(e_0)$. Prove that $f*g-f-g\in S_1(x)$ is a 1-boundary.

$z_0^m+z_1^m+z_2^m+z_3^m=0$ defines a surface in $P^3$. What argument is used to compute euler characteristic?

$f$ is a cycle since it is a loop, and since $H_1(point) = 0$, $f$ must then be a boundary.

Could someone explain to me what a Teichmuller Space is?

Errata for Bott Tu Differential Forms

Different definitions of (co)homology with local coefficients

Serre fibrations have HLP against all CW complexes

Crossing Number of $K_5$ on the Tubular Neighborhood of a Trefoil Knot

Can two Lie groups be "almost" homeomorphic?

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