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Results tagged with gt.geometric-topology
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user 44651
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
9
votes
3
answers
660
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Do we get a instanton $S^{3}$ if we do $1/n$ surgery on a knot in $S^{3}$?
Consider the following question:
Let $K\subset S^{3}$ be a nontrivial knot, and let $Y$ be the manifold obtained by doing $1/n$-surgery ($n\geq1$). Is it possible that the instanton Floer homology of …
- 9,580
6
votes
0
answers
155
views
Relation between different versions of Bar-Natan homology
In Bar-Natan's paper: Khovanov’s homology for tangles and cobordisms, he defined a deformation of Khovanov homology. Namely, for any $m\geq 0$, Bar-Natan's homology $BN^{m}(K)$ is obtained by tensorin …
- 13.6k
5
votes
2
answers
366
views
Ozsváth-Szabó's contact invariant on the Brieskorn sphere $\Sigma(2,3,6m+1)$
According to Theorem 1.7 of Mark-Tosun's paper, the Brieskorn sphere $\Sigma(2,3,6m+1)$ admits two tight contact structure $\xi_{i}\ (i=0,1)$. They are both Stein fillable and they are contactomorphic …
- 773
9
votes
1
answer
615
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Intuition for Szabo's geometric spectral sequence
In https://arxiv.org/abs/1010.4252, Szabo defines a link invariant $\hat{H}(L)$ which can be computed combinatorially from a link diagram and shows that there is a spectral sequence from Khovanov homo …
- 518
14
votes
2
answers
765
views
For a 3-manifold $Y$, when does $Y\times S^{1}$ admits a Riemannian metric with positive sca...
Let $Y$ be an orientable, smooth 3-manifold and let $X=Y\times S^{1}$. My question is that: when does $X$ admits a Riemannian metric with positive scalar curvature?
An obvious case is when $Y$ itsel …
- 68.8k
8
votes
0
answers
249
views
Exact triangle for monopole Floer homology with $\mathbb{Z}$-coefficient
Let $Y$ be oriented 3 manifold with torus boundary and let $\gamma_{j}$ (j=0,1,2) be three curves on its boundary with $\#(\gamma_{j}\cap \gamma_{j+1})=-1$. We denote by $Y_{j}$ the manifold obtained …
- 1,069
9
votes
1
answer
330
views
Essential Klein bottle in simply connected symplectic 4 manifolds
Consider the following question:
Let $X$ be a simply connected, symplectic 4-manifold. Does there exists a smoothly embedded Klein bottle $K\subset X$ such that the following conditions are both satis …
- 9,481
6
votes
1
answer
335
views
Embedded spheres in the K3 surface
Using the Seiberg-Witten theory, we know that every (smoothly) embedded $S^{2}$ in $K3$ with trivial normal bundle is null-homologous. We know we have a lot of interesting knotted $S^{2}$ inside $S^{4 …
- 36
7
votes
2
answers
280
views
What are known examples of a 3-manifold $Y$ embedded into $Y'\times I$ where $Y'$ is another...
The question I have is the following:
Let $Y,Y'$ be two integer homology 3-spheres. Can we embed $Y'$ into $Y\times I$ such that $Y'$ separates the two boundary components apart?
Do we know any nont …
- 19.4k
1
vote
0
answers
131
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Regularity of the taut foliation
In Eliashberg-Thurston's famous paper "Confoliations" Corollary 3.2.11, they proved that Irreducible three manifold with $b_{1}>0$ admits semi-fillable contact structure using Gabai's theorem in the p …
- 1,069
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: …
- 481