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Results tagged with knot-theory
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user 8345
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.
2
votes
Does annular Khovanov homology detect the unknot (in annulus)?
The answer is yes if we assume all the components of the link are null-homologous; see Yi Xie's preprint here. This is a combination of an annular version of singular instanton link homology and the …
- 1,723
4
votes
Algorithm for computing the Arf invariant of a knot
The well-known (see here) relations between the Arf invariant and the Alexander/Jones polynomials give you algorithms for computing the Arf invariant, if that's all you want.
But it sounds like wha …
- 1,723
8
votes
A fun game related to knot theory
Yes, every link can be obtained in this way. Here's an inefficient way to do it. Put the link in braid form (via Alexander's theorem); suppose that we have $b$ strands. We'll achieve each braid gen …
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