English

A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical

Geometric Topology 2016-07-20 v4

Abstract

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M. In this article, we prove that either the disk complex D(F) is contractible or F is critical. Hence, the topological index of F is two if F is topologically minimal.

Keywords

Cite

@article{arxiv.1402.4253,
  title  = {A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical},
  author = {Jungsoo Kim},
  journal= {arXiv preprint arXiv:1402.4253},
  year   = {2016}
}

Comments

20 pages, 11 figures. More detailed arguments and figures