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Results tagged with knot-theory
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user 167503
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.
6
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3
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Infinite family of different prime knots with trivial Alexander polynomial
I am looking for infinite families of prime knots that have all Alexander polynomial equals to 1. I wrote "families" (and not "family") since perhaps there are different constructions out there.
Moreo …
- 601
2
votes
Infinite family of different prime knots with trivial Alexander polynomial
Another family of examples is given by the "generalised Kinoshita-Terasaka" knots, here is a picture from Lickorish' "An introduction to Knot Theory".
Here $d$ is assumed to be even. Of course, this …
- 601
3
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0
answers
185
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Reshuffling power series (aka Melvin–Morton expansion in knot theory)
I am struggling to understand a statement which follows from some change of variables in a power series. I think that the context does not really matter here, so I will put it at the end of the questi …
- 601