The moduli space of two-convex embedded tori

In this short article, we investigate the topology of the moduli space of two-convex embedded tori S^n-1 × S¹ R n+1 We prove that for n 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 3 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.