Question

Why is the identity map of the circle not straight-line homotopic to a constant map?

score 1.5k · Answer 1 · 2026-04-13 19:38:48

1.5k

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Why is the identity map of the circle not straight-line homotopic to a constant map?

Published on 13 Apr 2026 - 19:38

score 1000 · Answer 2 · 2026-04-09 23:35:02

1000

Views

How do I show homotopy equivalence between two topological spaces?

Published on 09 Apr 2026 - 23:35

score 1.5k · Answer 3 · 2026-04-12 08:57:30

1.5k

Views

Jeffrey Strom, ''Modern Classical Homotopy Theory'', prerequesites and recommended knowledge

Published on 12 Apr 2026 - 8:57

score 96 · Answer 4 · 2026-05-11 05:07:46

96

Views

A question on the relation of truncation $\tau_{\leq n}$ to the internal hom adjunction of spectra

Published on 11 May 2026 - 5:07

score 112 · Answer 5 · 2026-04-16 12:28:40

112

Views

Question on the relation between the $n$-coskeleton functor and the internal hom-adjunction

Published on 16 Apr 2026 - 12:28

score 388 · Answer 6 · 2026-04-13 05:30:42

388

Views

H-space and fundamental group

Published on 13 Apr 2026 - 5:30

score 363 · Answer 7 · 2026-04-15 01:06:33

363

Views

A question about Homotopy (Michael Harris's recent book)

Published on 15 Apr 2026 - 1:06

score 126 · Answer 8 · 2026-04-10 01:25:43

126

Views

Does a cofiber sequence of CW complexes induce a cofiber sequence of skeleta?

Published on 10 Apr 2026 - 1:25

score 236 · Answer 9 · 2026-04-16 02:00:26

How to show the failure of the homotopy extension property for the pair $I=[0,1]$ and $A=\left\{ 0,1,\frac{1}{2},\frac{1}{3}...\right\}$?

score 74 · Answer 10 · 2026-04-12 13:54:37

74

Views

Not all retractions come from deformation retractions

Published on 12 Apr 2026 - 13:54

score 397 · Answer 11 · 2026-04-15 20:30:42

397

Views

Is the homotopy category cartesian closed?

Published on 15 Apr 2026 - 20:30

score 1.7k · Answer 12 · 2026-04-13 01:22:55

1.7k

Views

Closed, simply connected manifolds which are not spheres

Published on 13 Apr 2026 - 1:22

score 747 · Answer 13 · 2026-05-10 17:36:02

747

Views

Clarification regarding little n-discs operads

Published on 10 May 2026 - 17:36

score 239 · Answer 14 · 2026-05-10 15:03:12

239

Views

Well-definedness of first obstruction (to extending a map or homotopy of maps over the skeleta of a CW complex) lying in a nonzero group

Published on 10 May 2026 - 15:03

score 341 · Answer 15 · 2026-04-16 14:29:43

341

Views

Aspherical manifolds and their homotopy type

Published on 16 Apr 2026 - 14:29

List Question

Why is the identity map of the circle not straight-line homotopic to a constant map?

How do I show homotopy equivalence between two topological spaces?

Jeffrey Strom, ''Modern Classical Homotopy Theory'', prerequesites and recommended knowledge

A question on the relation of truncation $\tau_{\leq n}$ to the internal hom adjunction of spectra

Question on the relation between the $n$-coskeleton functor and the internal hom-adjunction

H-space and fundamental group

A question about Homotopy (Michael Harris's recent book)

Does a cofiber sequence of CW complexes induce a cofiber sequence of skeleta?

How to show the failure of the homotopy extension property for the pair $I=[0,1]$ and $A=\left\{ 0,1,\frac{1}{2},\frac{1}{3}...\right\}$?

Not all retractions come from deformation retractions

Is the homotopy category cartesian closed?

Closed, simply connected manifolds which are not spheres

Clarification regarding little n-discs operads

Well-definedness of first obstruction (to extending a map or homotopy of maps over the skeleta of a CW complex) lying in a nonzero group

Aspherical manifolds and their homotopy type

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