All Questions
Tagged with branched-covers gt.geometric-topology
9
questions
16
votes
3
answers
916
views
Maximal degree of a map between orientable surfaces
Suppose that $M$ and $N$ are closed connected oriented surfaces. It is well-known that if $f \colon M \to N$ has degree $d > 0$, then $\chi(M) \le d \cdot \chi(N)$.
What is an elementary proof of ...
- 1,085
4
votes
2
answers
325
views
Books for learning branched coverings
I am self-studying branched coverings. I read it from B. Maskit's Kleinian groups book. I want some more references for reading branched covers. In particular, I want to understand how to create ...
- 347
6
votes
3
answers
1k
views
Graphs from the point of view of Riemann surfaces
I was listening to the lecture "Graphs from the point of view of
Riemann surfaces" by Prof. Alexander Mednykh. I am looking for references for the basics of this topic. Any kind of ...
5
votes
1
answer
340
views
Thurston universe gates in knots: which invariant is it?
Today I discovered this nice video of a lecture by Thurston:
https://youtu.be/daplYX6Oshc
in which he explains how a knot can be turned into a "fabric for universes". For example, the unknot ...
- 1,954
15
votes
1
answer
778
views
$S^3$ as cyclic branched cover of itself
In Chapter One of his notes (March 2002) Thurston says:
If $K$ is the trivial knot the cyclic branched covers are $S^3$. It seems intuitively obvious (but it is not known) that this is the only ...
- 606
5
votes
3
answers
1k
views
Heegaard Floer Homology of double branched cover
The question is the following:
Let $K\subset S^{3}$ be a knot, consider the double branched cover $Y$ of $S^{3}$ over $K$. We know $Y$ has a unique spin structure $\mathfrak{s}$, now the question is: ...
- 1,059
5
votes
1
answer
1k
views
The cyclic branched covers of "simple" knots in $S^3$
Is there a convenient place in the literature where the geometric decompositions of cyclic branched covers of $S^3$ branched over "small" knots is recorded?
By small knots, I'm referring to things ...
- 43.5k
3
votes
1
answer
323
views
Classification of fiber-preserving branched covers between Seifert fibered integer homology spheres
Is there an easy classification (and proof) of the possible branched covers between Seifert fibered integer homology spheres which are fiber-preserving and branched over fibers (or at least what the ...
- 215
6
votes
2
answers
723
views
degenerating surface
Hi,
i have a sequence of immersed disc $u_n: \mathbb{D} \rightarrow \mathbb{R}^3$ which converge to a singular cover of the disc: $z^k$ for $k\geq 2$, moreprecisely $u_n \rightarrow z^k$ in $C^2(\...
- 924