  In this short article we investigate the topology of the moduli space of
two-convex embedded tori $S^{n-1}\times S^1\subset \mathbb{R}^{n+1}$. We prove
that for $n \geq 3$ this moduli space is path-connected, and that for $n = 2$
the connected components of the moduli space are in bijective correspondence
with the knot classes associated to the embeddings. Our proof uses a variant of
mean curvature flow with surgery developed in our earlier article
(arXiv:1607.05604) where neck regions are deformed to tiny strings instead of
being cut out completely, an approach which preserves the global topology,
embeddedness, as well as two-convexity.
