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