All Questions
Tagged with branched-covers 3-manifolds
4
questions
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 ...
4
votes
1
answer
218
views
Pre-images of Seifert surfaces are incompressible?
Consider a knot $K \subset S^3$ and let $M_K$ be the associated double branched cover. The pre-image $S$ of a Seifert surface is a surface without boundary inside $M_K$.
Can $S$ be incompressible? If ...
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 ...
5
votes
3
answers
1k
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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: ...