List questions from covering-spaces

Published on 29 Mar 2026 - 8:17

791

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Constructing covering space of surfaces

Published on 01 Nov 2015 - 18:29

582

Views

Universal cover of boundary

Published on 27 Mar 2026 - 5:01

1.3k

Views

Suppose $p:E\to B$ is a covering map and $B$ is connected. Prove that if $p^{-1}(\{b\})$ has n points $p^{-1}(\{b\})$ has n points for every $b\in B$

Published on 10 Nov 2015 - 1:50

1.9k

Views

Let $q: X\to Y$ and $r: Y\to Z$ be covering maps; let $p=r\circ q$. Show that if $r^{-1}(z)$ is finite for each $z\in Z$, then $p$ is a covering map.

Published on 12 Mar 2026 - 3:12

627

Views

Covering space of an abelian topological group is abelian if the covering map is a homomorphism

Published on 13 Nov 2015 - 21:05

580

Views

Covering a rectangle with circles

Published on 27 Mar 2026 - 12:03

2k

Views

Surface groups and subgroups of fundamental groups

Published on 15 Nov 2015 - 6:06

870

Views

Size of the deck transformation group

Published on 15 Nov 2015 - 20:39

938

Views

Covering map of the annulus

Published on 19 Nov 2015 - 18:48

199

Views

Determine a normal covering space

Published on 20 Nov 2015 - 16:58

2.2k

Views

Subgroup of $F_2$ with index 2 and 3

Published on 27 Mar 2026 - 9:55

289

Views

On a subgroup of the deck transformation of a covering space

Published on 24 Nov 2015 - 4:15

186

Views

How can I show that the composition of two coverings is also a covering?

Published on 26 Nov 2015 - 14:05

157

Views

Find a nonregular 3-fold covering space of the genus two closed orientable surface.

Published on 26 Nov 2015 - 16:11

List Question

What are the morphisms in the category of unramified coverings over a compact Riemann surface?

Constructing covering space of surfaces

Universal cover of boundary

Suppose $p:E\to B$ is a covering map and $B$ is connected. Prove that if $p^{-1}(\{b\})$ has n points $p^{-1}(\{b\})$ has n points for every $b\in B$

Let $q: X\to Y$ and $r: Y\to Z$ be covering maps; let $p=r\circ q$. Show that if $r^{-1}(z)$ is finite for each $z\in Z$, then $p$ is a covering map.

Covering space of an abelian topological group is abelian if the covering map is a homomorphism

Covering a rectangle with circles

Surface groups and subgroups of fundamental groups

Size of the deck transformation group

Covering map of the annulus

Determine a normal covering space

Subgroup of $F_2$ with index 2 and 3

On a subgroup of the deck transformation of a covering space

How can I show that the composition of two coverings is also a covering?

Find a nonregular 3-fold covering space of the genus two closed orientable surface.

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