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Results tagged with knot-theory
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user 90980
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.
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Space of the trivial long knot in the thickened surface
Let $F$ be a compact oriented surface and $x_0\in F$ a basepoint. Consider the set $\mathcal E=Emb_0(I,F\times I)$ of embeddings $\sigma\colon I\hookrightarrow F\times I$, $\sigma(\partial I)=\{x_0\}\ …
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Space of the trivial long knot in the thickened surface
Let us show that $\mathcal E=Emb_0(I,F\times I)\sim\Omega_0(F,x_0)$.
We start with R. Budney's remark.
Proposition. Let $F$ be a connected compact 2-manifold and $P(F)$ the pseudoisotopy group, i.e th …
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