List questions from algebraic-topology

Published on 26 Mar 2026 - 23:09

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Is there a Mayer-Vietoris sequence for an (uncountably) infinite collection of sets?

Published on 25 Mar 2026 - 22:26

889

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Why is the fundamental group of the Hopf link abelian but a two component unlink isn't

Published on 25 Mar 2026 - 9:39

169

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How is this circle in $S^1 \times D^2$ null-homotopic?

Published on 12 Feb 2019 - 3:26

505

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Let $X$ be a connected CW complex and $G$ a group such that every $\pi_1(X)\to G$ is trivial. Show that every $X\to K(G, 1)$ is nullhomotopic.

Published on 25 Mar 2026 - 9:29

1.1k

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Construction of Moore Space

Published on 25 Mar 2026 - 9:24

42

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$H_k (R^m, R^m \setminus 0) \cong H_k (S^m, S^m \setminus x)$?

Published on 01 Apr 2026 - 3:07

34

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$H_k (S^m, S^m \setminus x)\cong H_k (S^m, pt)$?

Published on 01 Apr 2026 - 3:10

40

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When does $(F,f): (X,A) \rightarrow (Y,B)$ induce isomorphisms on homology?

Published on 01 Apr 2026 - 3:06

98

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Finding an open simply connected subset in a punctured open simply connected set

Published on 26 Mar 2026 - 4:30

1.4k

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Homology of Klein bottle with Mayer-Vietoris

Published on 07 Apr 2026 - 18:46

64

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Examples of weak monoidal Quillen equivalences

Published on 03 Apr 2026 - 2:00

185

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Is the complex cobordism spectrum, $MU$, a finite spectrum?

Published on 06 Apr 2026 - 12:34

159

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An open cover of $\mathbb{R}^n$ and $\mathbb{C}^n$

Published on 02 Apr 2026 - 4:30

173

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Why does any connected closed $m$-manifold that can be embedded in $E^{m+1}$ bounds a compact connected $(m+1)$-manifold?

Published on 25 Mar 2026 - 6:12

List Question

Classification of contractible 4-manifolds

Is there a Mayer-Vietoris sequence for an (uncountably) infinite collection of sets?

Why is the fundamental group of the Hopf link abelian but a two component unlink isn't

How is this circle in $S^1 \times D^2$ null-homotopic?

Let $X$ be a connected CW complex and $G$ a group such that every $\pi_1(X)\to G$ is trivial. Show that every $X\to K(G, 1)$ is nullhomotopic.

Construction of Moore Space

$H_k (R^m, R^m \setminus 0) \cong H_k (S^m, S^m \setminus x)$?

$H_k (S^m, S^m \setminus x)\cong H_k (S^m, pt)$?

When does $(F,f): (X,A) \rightarrow (Y,B)$ induce isomorphisms on homology?

Finding an open simply connected subset in a punctured open simply connected set

Homology of Klein bottle with Mayer-Vietoris

Examples of weak monoidal Quillen equivalences

Is the complex cobordism spectrum, $MU$, a finite spectrum?

An open cover of $\mathbb{R}^n$ and $\mathbb{C}^n$

Why does any connected closed $m$-manifold that can be embedded in $E^{m+1}$ bounds a compact connected $(m+1)$-manifold?

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