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Results tagged with knot-theory
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user 44651
Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.
7
votes
2
answers
280
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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 …
- 1,069
9
votes
3
answers
660
views
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 …
- 1,069
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 …
- 1,069
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