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Results tagged with knot-theory
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user 31434
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.
9
votes
integer surgeries on knots
Lens spaces of orders 58 and 83 may be obtained by integral surgeries on torus knot; see Moser's "Elementary surgeries on torus knots" which gives the classification up to homeomorphism. (Mind Moser's …
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4
votes
1-Bridge Braids in Solid Tori (Berge-Gabai knots), dual knots, & knot exteriors
For Question #1:
As you acknowledge, Berge already gives an answer to Question #1. Using his notation, this is summarized in Table 2 of his paper "The knots in $D^2 \times S^1$ which have nontrivial …
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4
votes
Homology torsion in the double branched cover of a tangle?
Yes. For example, start with the exterior of the Whitehead link and do p/q filling on one component where p is odd. This manifold has p torsion and is the double branched cover of a two strand tang …
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2
votes
Genus one fibered links
Agol's comment works to give 3 component fibered links with genus 1 fiber, but we can dial it back a bit further.
The connect sum of a Hopf band and its mirror is a 3-component link of unknots wit …
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