The moduli space of two-convex embedded tori
International Mathematics Research Notices
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In this short article, we investigate the topology of the moduli space of two-convex embedded tori [formula]. We prove that for [formula] this moduli space is path connected, and that for [formula] 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  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.
AuthorsBUZANO, R; Haslhofer, R; Hershkovits, O
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