Question

Topology - Fundamental group proof - Path homotopy

score 233 · Answer 1 · 2026-04-10 11:26:40

233

Views

Topology - Fundamental group proof - Path homotopy

Published on 10 Apr 2026 - 11:26

score 132 · Answer 2 · 2026-04-09 04:35:09

132

Views

The canonical null-homotopy of the fiber sequence $F(f)\to X\to Y$.

Published on 09 Apr 2026 - 4:35

score 390 · Answer 3 · 2026-03-25 09:53:47

390

Views

For $n \ge 3$, is $\mathbb R^n \setminus A$ simply connected for any countable set $A$?

Published on 25 Mar 2026 - 9:53

score 100 · Answer 4 · 2026-03-25 09:49:24

100

Views

Simple connected ness of $\mathbb R^n$ minus a compact line segment , for $n \ge 3$

Published on 25 Mar 2026 - 9:49

score 46 · Answer 5 · 2026-03-25 11:24:33

46

Views

For a vector subspace $W$ of $\mathbb R^n$, where $n \ge 4$ and $\dim W\le n-3$, is $\mathbb R^n\setminus W $ simply connected?

Published on 25 Mar 2026 - 11:24

score 258 · Answer 6 · 2026-03-29 15:31:19

258

Views

Do homotopy pullbacks respect homotopy equivalences?

Published on 29 Mar 2026 - 15:31

score 111 · Answer 7 · 2026-03-29 13:40:48

111

Views

Show that, if $u: B \rightarrow C$ and $v:D \rightarrow E$ are cochain maps, then $vfu$ and $vgu$ are chain homotopic.

Published on 29 Mar 2026 - 13:40

score 42 · Answer 8 · 2026-03-27 06:01:41

42

Views

Terminology on comparison of homotopy types

Published on 27 Mar 2026 - 6:01

score 106 · Answer 9 · 2026-04-01 01:17:31

106

Views

Meromorphic functions and the homotopy principle? What gives?

Published on 01 Apr 2026 - 1:17

score 105 · Answer 10 · 2026-03-25 07:45:49

105

Views

Let $H=p_*(\pi_1(E,e_0))$. show that there is a bijection between the sets $\pi_1(B,b_0)/H$ and $p^{-1}(b_0)$. It follows that the number of sheets

Published on 25 Mar 2026 - 7:45

score 913 · Answer 11 · 2026-03-29 18:53:40

913

Views

Homotopy Groups of $S^l \vee S^k$

Published on 29 Mar 2026 - 18:53

score 640 · Answer 12 · 2026-03-25 00:02:21

640

Views

When does conservative imply faithful for functors?

Published on 25 Mar 2026 - 0:02

score 1.2k · Answer 13 · 2026-04-02 18:43:00

1.2k

Views

Show that if $Y$ is path connected, then there is only one homotopy class of maps of $[0,1]$ into Y

Published on 02 Apr 2026 - 18:43

score 58 · Answer 14 · 2026-04-02 20:25:24

58

Views

Prove that $f \simeq 0: X → \mathbb R$ for any map $f : X → \mathbb R$

Published on 02 Apr 2026 - 20:25

score 132 · Answer 15 · 2026-03-25 01:18:23

132

Views

How are the sheets of $y^3 = x(x-1)(x+1)$ arranged?

Published on 25 Mar 2026 - 1:18

List Question

Topology - Fundamental group proof - Path homotopy

The canonical null-homotopy of the fiber sequence $F(f)\to X\to Y$.

For $n \ge 3$, is $\mathbb R^n \setminus A$ simply connected for any countable set $A$?

Simple connected ness of $\mathbb R^n$ minus a compact line segment , for $n \ge 3$

For a vector subspace $W$ of $\mathbb R^n$, where $n \ge 4$ and $\dim W\le n-3$, is $\mathbb R^n\setminus W $ simply connected?

Do homotopy pullbacks respect homotopy equivalences?

Show that, if $u: B \rightarrow C$ and $v:D \rightarrow E$ are cochain maps, then $vfu$ and $vgu$ are chain homotopic.

Terminology on comparison of homotopy types

Meromorphic functions and the homotopy principle? What gives?

Let $H=p_*(\pi_1(E,e_0))$. show that there is a bijection between the sets $\pi_1(B,b_0)/H$ and $p^{-1}(b_0)$. It follows that the number of sheets

Homotopy Groups of $S^l \vee S^k$

When does conservative imply faithful for functors?

Show that if $Y$ is path connected, then there is only one homotopy class of maps of $[0,1]$ into Y

Prove that $f \simeq 0: X → \mathbb R$ for any map $f : X → \mathbb R$

How are the sheets of $y^3 = x(x-1)(x+1)$ arranged?

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