Question

$p:X\rightarrow Y$ is a cover map, $y\in Y$ and $|p^{-1}(y)|<\infty$ then $|p^{-1}(y')|=|p^{-1}(y)|$ for all $y'\in Y$

score 33 · Answer 1 · 2026-03-25 09:43:07

33

Views

$p:X\rightarrow Y$ is a cover map, $y\in Y$ and $|p^{-1}(y)|<\infty$ then $|p^{-1}(y')|=|p^{-1}(y)|$ for all $y'\in Y$

Published on 25 Mar 2026 - 9:43

score 881 · Answer 2 · 2026-03-25 12:53:01

881

Views

Inclusion of path connected component induces isomorphism between fundamental groups.

Published on 25 Mar 2026 - 12:53

score 519 · Answer 3 · 2026-03-25 12:50:10

519

Views

Fundamental group of space form by gluing boundary of Mobius band to $S^1 \vee S^1$

Published on 25 Mar 2026 - 12:50

score 102 · Answer 4 · 2018-05-13 08:52:09

102

Views

Is there a natural homorphism $\pi_1(X/G) \rightarrow G$?

Published on 13 May 2018 - 8:52

score 275 · Answer 5 · 2018-05-14 03:15:28

275

Views

Calculate the linking number of two loops in $S^3$

Published on 14 May 2018 - 3:15

score 129 · Answer 6 · 2018-05-14 04:29:38

Let $X$ be the complex obtained by gluing two discs to $S^1$ via maps of relatively prime degree. $X$ is simply connected.

score 136 · Answer 7 · 2018-05-14 13:26:36

If $A$ and $B$ are bounded simply connected open subsets of $\mathbb{R}^2$ then a connected component $C$ of $A\cap B$ is simply connected?

score 51 · Answer 8 · 2026-03-25 21:45:08

51

Views

Intersection between $\mathbb{R}P^2$ and $\mathbb{C}P^1$

Published on 25 Mar 2026 - 21:45

score 705 · Answer 9 · 2026-03-22 23:38:54

705

Views

Homology of free loop space and Hochschild cohomology

Published on 22 Mar 2026 - 23:38

score 441 · Answer 10 · 2026-03-29 20:21:46

441

Views

Cellular Homology of the quotient of $S^1\times D^2$ by its boundary

Published on 29 Mar 2026 - 20:21

score 659 · Answer 11 · 2018-05-14 19:00:37

659

Views

The $n-1$ homology group of $U\setminus\{x\}\subset \mathbb{R}^n$ where $U$ is open.

Published on 14 May 2018 - 19:00

score 113 · Answer 12 · 2018-05-14 19:54:35

113

Views

If $q\circ p$ and $q$ are covering maps then $p$ is also a covering map.

Published on 14 May 2018 - 19:54

score 126 · Answer 13 · 2026-03-25 04:39:35

126

Views

Sylow subgroups/subgroup lattices in algebraic topology?

Published on 25 Mar 2026 - 4:39

score 65 · Answer 14 · 2026-03-25 07:52:08

65

Views

Why do I need to specify some "continuous" choice of paths

Published on 25 Mar 2026 - 7:52

score 248 · Answer 15 · 2026-03-25 00:06:33

248

Views

Why do linear transforms act on loops in the torus in this way?

Published on 25 Mar 2026 - 0:06

List Question

$p:X\rightarrow Y$ is a cover map, $y\in Y$ and $|p^{-1}(y)|<\infty$ then $|p^{-1}(y')|=|p^{-1}(y)|$ for all $y'\in Y$

Inclusion of path connected component induces isomorphism between fundamental groups.

Fundamental group of space form by gluing boundary of Mobius band to $S^1 \vee S^1$

Is there a natural homorphism $\pi_1(X/G) \rightarrow G$?

Calculate the linking number of two loops in $S^3$

Let $X$ be the complex obtained by gluing two discs to $S^1$ via maps of relatively prime degree. $X$ is simply connected.

If $A$ and $B$ are bounded simply connected open subsets of $\mathbb{R}^2$ then a connected component $C$ of $A\cap B$ is simply connected?

Intersection between $\mathbb{R}P^2$ and $\mathbb{C}P^1$

Homology of free loop space and Hochschild cohomology

Cellular Homology of the quotient of $S^1\times D^2$ by its boundary

The $n-1$ homology group of $U\setminus\{x\}\subset \mathbb{R}^n$ where $U$ is open.

If $q\circ p$ and $q$ are covering maps then $p$ is also a covering map.

Sylow subgroups/subgroup lattices in algebraic topology?

Why do I need to specify some "continuous" choice of paths

Why do linear transforms act on loops in the torus in this way?

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