All Questions
8 questions
4
votes
1
answer
152
views
Topological type of complement of Heegaard curves in Heegaard surface $(\Sigma - \alpha - \beta)$
Suppose $(\Sigma, \alpha, \beta)$ is a genus-$g$ Heegaard diagram for a closed, oriented $3$-manifold $Y$, i.e. $\Sigma$ is an orientable genus-$g$ surface, and $(\alpha_1, \dots, \alpha_g)$ and $(\...
- 281
5
votes
2
answers
1k
views
Heegard diagrams for three-manifolds
I have a basic question about the Heegaard diagrams involved in providing a framework
for calculation of Floer-Homology of three-manifolds.
Typically such diagrams look like Figure 1 and Figure 2 here ...
- 6,018
16
votes
1
answer
632
views
Three-manifolds having a Reebless foliation but not a taut one
A straightforward argument reveals that a taut foliation is Reebless, and of course there are many examples of Reebless foliations that are not taut. I guess that there are many examples of three-...
- 606
3
votes
0
answers
181
views
Definition of the dual spider number and the formula for the first chern class of the triangle
In the process of trying to understand various maps in Heegaard Floer homology I got stuck on the definition of the dual spider number, which, it seems to me, has a combinatorial definition directly ...
- 1,000
7
votes
1
answer
448
views
In the definition of the Heegard Floer surgery exact triangle, what exactly is the correspondence between Whitney triangles and periodic domains?
I'm reading Osváth-Szabó's notes on Heegard Floer homology, in particular about the surgery exact triangle.
On page 14 (numbered 42 on the document), they describe an isomorphism between the space of ...
- 155
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: ...
- 1,069
12
votes
1
answer
907
views
Wanted: a nontrivial weakly inadmissible Heegaard diagram
This is a question asked by a student in my lecture. After drawing pictures for awhile, I thought it was a good one. I seek a nontrivial example of a pointed Heegaard diagram $(\Sigma,\mathbf{\alpha},\...
7
votes
2
answers
674
views
heegard diagram
It seems like there is an algorithm to find the Heegard diagram of a 3 manifold obtained by surgery on a link. Also someone told me I can find it in the Gompf and Stipciz's book. But I could not find ...
- 155