Semi-isotopic knots

Abstract

A $\text{knot}$ is a possibly wild simple closed curve in $S^3$. A knot $J$ is $\text{semi-isotopic}$ to a knot $K$ if there is an annulus $A$ in $S^3\times [0,1]$ such that $A\cap (S^3\times \{0,1\})=\partial A=(J\times \{0\})\cup (K\times \{1\})$ and there is a homeomorphism $e:S^1\times [0,1)\to A-(K\times \{1\})$ such that $e(S^1\times \{t\})\subset S^3\times \{t\}$ for every $t\in [0,1)$. $\text{Theorem.}$ Every knot is semi-isotopic to an unknot.

10 pages, 5 figures, minor formatting change, minor typo correct