The moduli space of two-convex embedded spheres
Differential Geometry
2021-10-14 v2 Geometric Topology
Abstract
We prove that the moduli space of 2-convex embedded n-spheres in R^{n+1} is path-connected for every n. Our proof uses mean curvature flow with surgery and can be seen as an extrinsic analog to Marques' influential proof of the path-connectedness of the moduli space of positive scalar curvature metics on three-manifolds.
Cite
@article{arxiv.1607.05604,
title = {The moduli space of two-convex embedded spheres},
author = {Reto Buzano and Robert Haslhofer and Or Hershkovits},
journal= {arXiv preprint arXiv:1607.05604},
year = {2021}
}
Comments
v2: We have revised the introduction to better reflect the similarities and differences between our work and related work in the intrinsic case by Marques (Ann. of Math. 2012)