On the topological rigidity of self shrinkers in ${\mathbb{R}}^3$

In this note we show that compact self shrinkers in ${\mathbb{R}}^3$ are “topologically standard” in that any genus $g$ compact self shrinker is ambiently isotopic to the standard genus $g$ embedded surface in ${\mathbb{R}}^3$. As a consequence self shrinking tori are unknotted.