English

The disk complex and topologically minimal surfaces in the 3-sphere

Geometric Topology 2020-04-23 v3

Abstract

We show that the disk complex of a genus g>1g>1 Heegaard surface for the 3-sphere is homotopy equivalent to a wedge of (2g2)(2g-2)-dimensional spheres. This implies that genus g>1g>1 Heegaard surfaces for the 3-sphere are topologically minimal with index 2g12g-1.

Keywords

Cite

@article{arxiv.1912.03329,
  title  = {The disk complex and topologically minimal surfaces in the 3-sphere},
  author = {Marion Campisi and Luis Torres},
  journal= {arXiv preprint arXiv:1912.03329},
  year   = {2020}
}
R2 v1 2026-06-23T12:38:31.528Z