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Results tagged with knot-theory
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user 109329
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.
4
votes
1
answer
316
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On the genus of thin knots and the degree of the Alexander polynomial
I came across this papper by JA Baldwin which presents a combinatorial definition for the knot Floer homology.
At a certain paragraph of the third page the author makes the next statement: the genus …
- 205
4
votes
1
answer
157
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Twisting equivalent links and the isotopy type of the resulting links
Take any link $L_1$ with an unknotted component
$K$, cut along the disk bounded by K (which usually intersects some of the
other components of $L_1$ transversally ), twist n times, and reglue. Let us …
- 205
0
votes
1
answer
122
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Homogeneous links and crossings smoothing
Let $L$ be an oriented homogeneous link and let $D$ be an oriented diagram of $L$ wich is not necessarily a homogeneous diagram. Fix some crossing $c$ in $D$ and construct the diagram $D_0$ by smoothi …
- 205