Question

$\pi_3(Sp(N))=\mathbb{Z}$, $\pi_4(Sp(N))=\mathbb{Z}_2$, $\pi_5(Sp(N))=\mathbb{Z}_2$?

score 79 · Answer 1 · 2026-03-25 08:00:43

79

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$\pi_3(Sp(N))=\mathbb{Z}$, $\pi_4(Sp(N))=\mathbb{Z}_2$, $\pi_5(Sp(N))=\mathbb{Z}_2$?

Published on 25 Mar 2026 - 8:00

score 214 · Answer 2 · 2026-03-25 01:37:47

214

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Mapping Class Group of Knot Complements and Their Heegaard Splitting

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score 134 · Answer 3 · 2026-04-13 00:47:39

134

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Relationship between universal vector bundles and principal $O(n)$ bundles?

Published on 13 Apr 2026 - 0:47

score 285 · Answer 4 · 2026-04-11 16:12:56

285

Views

Bases and pseudo-bases in topological spaces

Published on 11 Apr 2026 - 16:12

score 31 · Answer 5 · 2026-04-13 03:51:47

31

Views

Nontrivial example of closed set relative to subspace but not with respect to original space

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score 2.1k · Answer 6 · 2026-03-25 12:28:09

2.1k

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Interesting questions (with answers) about concepts in topology for an amateur audience

Published on 25 Mar 2026 - 12:28

score 164 · Answer 7 · 2026-04-09 02:46:32

164

Views

If $X$ and $Y$ are subspaces of $Z$, $X \cong Y$ and $X$ is a retract of $Z$, is $Y$ also a retract of $Z$?

Published on 09 Apr 2026 - 2:46

score 318 · Answer 8 · 2018-08-14 12:39:35

318

Views

Difference between metric spaces and metrizable spaces (Munkres)

Published on 14 Aug 2018 - 12:39

score 40 · Answer 9 · 2026-04-09 04:33:09

40

Views

proving $(\mathbb{B}^2 \times \{0 \}) \bigcup (\mathbb{S}^1 \times [0, \infty))$ is a retract of $\mathbb{R}^3$

Published on 09 Apr 2026 - 4:33

score 49 · Answer 10 · 2018-08-14 15:21:15

49

Views

Does $x_n\to x$ $\iff \pi_\alpha (x_n)\to \pi_\alpha (x)$ always true?

Published on 14 Aug 2018 - 15:21

score 1k · Answer 11 · 2026-04-10 19:54:32

1k

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Why do we require that a perfect set is closed?

Published on 10 Apr 2026 - 19:54

score 238 · Answer 12 · 2026-04-03 16:13:00

238

Views

Prove that $I^2/\partial I^2$ is homeomorphic to $\mathbb{S}^2$

Published on 03 Apr 2026 - 16:13

score 72 · Answer 13 · 2018-08-14 16:50:33

For any $n \in \Bbb N$ , does there exist $A \subset \Bbb R$ such that $A^1,A^2,\ldots,A^{n-1}$ are non-empty and $A^n = \emptyset$?

score 857 · Answer 14 · 2026-04-11 04:02:04

857

Views

Is every finitely generated group the fundamental group of some finite topological space?

Published on 11 Apr 2026 - 4:02

score 143 · Answer 15 · 2026-03-25 20:42:13

143

Views

Understand the suspension (topology) and some Lie group examples

Published on 25 Mar 2026 - 20:42

List Question

$\pi_3(Sp(N))=\mathbb{Z}$, $\pi_4(Sp(N))=\mathbb{Z}_2$, $\pi_5(Sp(N))=\mathbb{Z}_2$?

Mapping Class Group of Knot Complements and Their Heegaard Splitting

Relationship between universal vector bundles and principal $O(n)$ bundles?

Bases and pseudo-bases in topological spaces

Nontrivial example of closed set relative to subspace but not with respect to original space

Interesting questions (with answers) about concepts in topology for an amateur audience

If $X$ and $Y$ are subspaces of $Z$, $X \cong Y$ and $X$ is a retract of $Z$, is $Y$ also a retract of $Z$?

Difference between metric spaces and metrizable spaces (Munkres)

proving $(\mathbb{B}^2 \times \{0 \}) \bigcup (\mathbb{S}^1 \times [0, \infty))$ is a retract of $\mathbb{R}^3$

Does $x_n\to x$ $\iff \pi_\alpha (x_n)\to \pi_\alpha (x)$ always true?

Why do we require that a perfect set is closed?

Prove that $I^2/\partial I^2$ is homeomorphic to $\mathbb{S}^2$

For any $n \in \Bbb N$ , does there exist $A \subset \Bbb R$ such that $A^1,A^2,\ldots,A^{n-1}$ are non-empty and $A^n = \emptyset$?

Is every finitely generated group the fundamental group of some finite topological space?

Understand the suspension (topology) and some Lie group examples

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