All Questions
10 questions
1
vote
1
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175
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Does fiber bundles admits good properties of covering spaces?
Let $X$ and $Y$ be non compact complex manifolds and $f:X\to Y$ be a holomorphic fiber bundle with fibers $F$ such that $f^*:\pi_1(X)\to\pi_1(Y)$ is injective and let for any $f_1,f_2\in F$ there ...
- 585
0
votes
1
answer
1k
views
What is definition of branched covering?
What is definition of branched covering in the page 10 of following paper ?
In Hatcher, Allen; Lochak, Pierre; Schneps, Leila, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. ...
- 119
12
votes
1
answer
508
views
Construction of the universal covering space via compact-open topology
This is a re-post of a question I asked a month ago on MSE, but unfortunately didn't receive any answers. I'm hoping someone could help me with it. Here it goes:
Recently I've been self-studying the ...
- 285
14
votes
0
answers
784
views
Covering image of a connected CW-complex need not be a CW-complex
This question is already asked here MSE, and there is an answer based on some conjecture (probably still open). I am posting the same question for a counterexample (if any, not based on such unsolved ...
- 632
3
votes
1
answer
352
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If $X, Y$ are topological spaces, with $Y$ being a k-space, and $f : X \to Y$ is a proper covering map, is $X$ necessarily a k-space?
A k-space is a compactly generated Hausdorff topological space. (I used the terminology "k-space" in the question, in order keep the question within the limit of 150 characters.)
Note that under the ...
- 311
3
votes
2
answers
1k
views
Nonpathological nonnormal covering space
A topological covering $p : \tilde{X} \to X$ is normal when the group of deck transformations acts transitively on the fibers of $p$. This is equivalent to the fact that $p_* (\pi (\tilde{X}, \tilde{x}...
- 2,824
6
votes
1
answer
477
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Universal covering and double cover functors
Initially posted on MSE
Let $\mathsf{CW}$ be the category of CW-complexes and $\mathsf{CW}_*$ that of pointed CW-complexes (possibly disconnected, one basepoint in each component). I would like to ...
- 319
13
votes
4
answers
4k
views
Universal covering space for non-semilocally simply connected spaces
Consider a topological space $X$. Let us consider a universal covering space to be a covering $ p : \tilde{X} \rightarrow X$ which is a covering of all other covering spaces. (Perhaps I should call ...
- 1,162
6
votes
1
answer
967
views
Lifting local compactness to a covering space
(I decided to repost this from MathSE, since the question seems to not be as easy as I had thought)
NB: In this question, local compactness is used in its weak form, i.e. in a locally compact space, ...
- 2,389
10
votes
1
answer
2k
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Is a space with no covering spaces simply connected?
Suppose $X$ is a path connected space such that every connected covering space of $X$ is trivial (1-fold.) Must $X$ be simply connected?
Intuitively, the answer seems to be no (imagine taking a disk,...
- 713