Question

A map $h:S^1\to X$ Induces a Trivial Homomorphism of Fundamental Groups Iff it is Nullhomotopic.

score 2.3k · Answer 1 · 2026-03-25 07:21:57

2.3k

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A map $h:S^1\to X$ Induces a Trivial Homomorphism of Fundamental Groups Iff it is Nullhomotopic.

Published on 25 Mar 2026 - 7:21

score 159 · Answer 2 · 2026-03-27 03:43:05

159

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homology of mapping telescope of a monoid

Published on 27 Mar 2026 - 3:43

score 53 · Answer 3 · 2026-04-15 23:50:58

53

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Lifting of certain $S^1$ valued maps

Published on 15 Apr 2026 - 23:50

score 241 · Answer 4 · 2026-03-25 19:10:51

241

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question about "Homology fibrations and the group completion theorem"

Published on 25 Mar 2026 - 19:10

score 313 · Answer 5 · 2026-03-25 07:48:22

313

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Fundamental groupoid of a contractible space

Published on 25 Mar 2026 - 7:48

score 81 · Answer 6 · 2026-03-26 01:04:35

81

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pontrjagin ring of the homology of iterated loop suspension

Published on 26 Mar 2026 - 1:04

score 55 · Answer 7 · 2026-04-15 09:56:04

55

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What is the connection between $\widehat{\mathbb Q G}$ and distributions near the identity of $G$?

Published on 15 Apr 2026 - 9:56

score 66 · Answer 8 · 2026-04-13 06:45:22

66

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Why are chains topologically analoguous to distributions?

Published on 13 Apr 2026 - 6:45

score 302 · Answer 9 · 2026-04-11 00:36:27

302

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Spaces $X$ and $Y$ with $[Z, X]_{\bullet} \cong [Z, Y]_{\bullet}$ for all cogroup objects $Z$ in $\mathsf{hTop}_{\bullet}$

Published on 11 Apr 2026 - 0:36

score 320 · Answer 10 · 2026-03-25 19:11:18

320

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the geometric realization of a simplicial set is contractible

Published on 25 Mar 2026 - 19:11

score 427 · Answer 11 · 2026-04-12 06:51:36

427

Views

Example of topological spaces with continuous bijections that are not homotopy equivalent

Published on 12 Apr 2026 - 6:51

score 534 · Answer 12 · 2026-04-11 23:36:39

534

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Homotopy equivalences between some sphere-based spaces (quotient of spheres, bouquet of spheres, difference of spheres)

Published on 11 Apr 2026 - 23:36

score 1.1k · Answer 13 · 2026-04-15 09:42:08

1.1k

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Homotopy equivalence of $S^{2} \vee S^1$ to $S^{2} \cup A$ where A is a line segment joining noth and south poles

Published on 15 Apr 2026 - 9:42

score 283 · Answer 14 · 2026-03-25 19:11:48

283

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homomorphism of $H$-spaces between a monoid and loop space of its classifying space

Published on 25 Mar 2026 - 19:11

score 285 · Answer 15 · 2026-04-16 19:44:56

285

Views

Lift of $z^2$ map $S^1 \to S^1$

Published on 16 Apr 2026 - 19:44

List Question

A map $h:S^1\to X$ Induces a Trivial Homomorphism of Fundamental Groups Iff it is Nullhomotopic.

homology of mapping telescope of a monoid

Lifting of certain $S^1$ valued maps

question about "Homology fibrations and the group completion theorem"

Fundamental groupoid of a contractible space

pontrjagin ring of the homology of iterated loop suspension

What is the connection between $\widehat{\mathbb Q G}$ and distributions near the identity of $G$?

Why are chains topologically analoguous to distributions?

Spaces $X$ and $Y$ with $[Z, X]_{\bullet} \cong [Z, Y]_{\bullet}$ for all cogroup objects $Z$ in $\mathsf{hTop}_{\bullet}$

the geometric realization of a simplicial set is contractible

Example of topological spaces with continuous bijections that are not homotopy equivalent

Homotopy equivalences between some sphere-based spaces (quotient of spheres, bouquet of spheres, difference of spheres)

Homotopy equivalence of $S^{2} \vee S^1$ to $S^{2} \cup A$ where A is a line segment joining noth and south poles

homomorphism of $H$-spaces between a monoid and loop space of its classifying space

Lift of $z^2$ map $S^1 \to S^1$

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