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Results tagged with knot-theory
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user 30679
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.
3
votes
Surgery along an arc connecting the components of a $2$-component link gives the unknot
A recentish paper of mine (which generalizes portions of Scharlemann's and Eudave-Munoz's work) also addresses this question.
MR3192616 Taylor, Scott A. Comparing 2-handle additions to a genus 2 bo …
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4
votes
Accepted
Classification of tangles?
As Sam Nead points out, there is a relationship between spatial graphs and tangles obtained by drilling out one edge of a spatial graph having two vertices or drilling out the vertex of a spatial grap …
- 574
2
votes
Reference for a theorem on crossing changes of links
The reference is given in the paper you cite:
M. Eudave-Mun ̃oz, Primeness and sums of tangles, Trans. Am. Math. Soc. 306, 773-790 (1988)
The arguments are purely combinatorial, but there should be a …
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7
votes
Is a knotted trivalent graph determined by its set of unzips?
This is really more of a comment, but here goes:
The question you ask is "dual" to this question: Suppose you have two theta graphs $\theta_1$ and $\theta_2$ such that for each edge $e_1$ of $\theta_ …
4
votes
Accepted
Handlebody decomposition of a 3-manifold adapted to a link
Take a Heegaard splitting of the link exterior and then glue in solid tori with your link components as cores. The Heegaard splitting survives as a Heegaard splitting of the filled manifold and since …
- 574
5
votes
Knot theory in handlebodies of arbitrary genus
If you mean adding 1 and 2 handles to the boundary of the ball, that will never change the (non)triviality of the knot in the 3-ball. On the other hand, perhaps the notion of tunnel number is what you …
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