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Results tagged with knot-theory
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user 11324
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.
1
vote
1
answer
278
views
crookedness of convex curves (milnor)
hello,
I'm currently reading On the Total Curvature of Knots and am trying to understand one of the lemmas in it (3.3)
A closed polygon $P$ in $H^2$ is convex if and only if for every $b$ either $\m …
- 41
2
votes
1
answer
723
views
isotopy doesn't make sense (Milnor)
hello,
I am having a hard time following this isotopy put forth by Milnor in On the Total Curvature of Knots
For each $c$ and $p$ in
$\mathbb{R}^{n-1}$ such that $\|c-p\|
> < r$, there is an is …
- 41