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Results tagged with knot-theory
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user 1956
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.
22
votes
3
answers
5k
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Why is it so hard to implement Haken's Algorithm for knot theory?
Why is it so hard to implement Haken's Algorithm for recognizing whether a knot is unknotted? (Is there a computer implementation of this algorithm?)
- 455
1
vote
1
answer
834
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Handle slides homeomorphism
For handle decomposition of surface, suppose I have a twisted 1-handle(twisted only once) adjacent to an isolated pair of linked handles, is the handle slide operation enough to move the previous one …
- 455
8
votes
3
answers
2k
views
Whitehead doubles of any knots
I was curious about the fact that the Whitehead doubles of all knots have Alexander polynomial equal to 1, which is the same as a unknot. How to prove this?
- 455