Question

Let x,y,z,u be loops in a point p: x•y and z•u are homotopic and y is homotopic to u then x is homotopic to z

score 21 · Answer 1 · 2026-03-25 14:25:07

21

Views

Let x,y,z,u be loops in a point p: x•y and z•u are homotopic and y is homotopic to u then x is homotopic to z

Published on 25 Mar 2026 - 14:25

score 343 · Answer 2 · 2026-04-29 12:48:00

343

Views

Is the homology of the based loop space of a compact globally symmetric space a polynomial ring?

Published on 29 Apr 2026 - 12:48

score 607 · Answer 3 · 2026-04-16 16:43:36

607

Views

How to explain why free loop space, or based loop space, is infinite dimensional to non-math people.

Published on 16 Apr 2026 - 16:43

score 498 · Answer 4 · 2026-04-30 10:48:30

498

Views

lifting a closed curve

Published on 30 Apr 2026 - 10:48

score 44 · Answer 5 · 2026-04-15 08:09:34

44

Views

existance of loop with finitely many point of intersection

Published on 15 Apr 2026 - 8:09

score 148 · Answer 6 · 2026-04-13 03:28:25

148

Views

For compact surface $M$ and loop $f$ there exists a surjection $\phi: H_1(M) \to \mathbb{Z}/8\mathbb{Z}$ such that $f \notin \ker(\phi)$

Published on 13 Apr 2026 - 3:28

score 482 · Answer 7 · 2026-04-14 00:08:10

482

Views

On loop space of a product

Published on 14 Apr 2026 - 0:08

score 673 · Answer 8 · 2026-04-14 18:30:40

673

Views

Loop spaces have the homotopy type of a topological groups

Published on 14 Apr 2026 - 18:30

score 238 · Answer 9 · 2026-05-10 14:07:10

238

Views

What is the map $\Sigma K(G,n) \to K(G,n+1)$?

Published on 10 May 2026 - 14:07

score 1.5k · Answer 10 · 2026-04-12 14:26:01

1.5k

Views

When is the free loop space simply connected?

Published on 12 Apr 2026 - 14:26

score 138 · Answer 11 · 2026-04-13 20:49:21

138

Views

$E_{\infty}$ spaces are $A_{\infty}$ spaces

Published on 13 Apr 2026 - 20:49

score 176 · Answer 12 · 2026-05-10 13:44:56

176

Views

What is a thin loop?

Published on 10 May 2026 - 13:44

score 452 · Answer 13 · 2026-04-13 05:23:45

452

Views

Free loop space of classifying space as a disjoint union of classifying spaces of centralizer proof reference request.

Published on 13 Apr 2026 - 5:23

score 167 · Answer 14 · 2026-04-01 09:33:48

167

Views

Definition of an infinite loop space

Published on 01 Apr 2026 - 9:33

score 78 · Answer 15 · 2026-03-25 16:02:51

78

Views

Are the base points of freely homotopic loops guaranteed to be in the same path-component?

Published on 25 Mar 2026 - 16:02

List Question

Let x,y,z,u be loops in a point p: x•y and z•u are homotopic and y is homotopic to u then x is homotopic to z

Is the homology of the based loop space of a compact globally symmetric space a polynomial ring?

How to explain why free loop space, or based loop space, is infinite dimensional to non-math people.

lifting a closed curve

existance of loop with finitely many point of intersection

For compact surface $M$ and loop $f$ there exists a surjection $\phi: H_1(M) \to \mathbb{Z}/8\mathbb{Z}$ such that $f \notin \ker(\phi)$

On loop space of a product

Loop spaces have the homotopy type of a topological groups

What is the map $\Sigma K(G,n) \to K(G,n+1)$?

When is the free loop space simply connected?

$E_{\infty}$ spaces are $A_{\infty}$ spaces

What is a thin loop?

Free loop space of classifying space as a disjoint union of classifying spaces of centralizer proof reference request.

Definition of an infinite loop space

Are the base points of freely homotopic loops guaranteed to be in the same path-component?

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