High Distance Heegaard Splittings via Dehn Twists
Geometric Topology
2014-10-01 v1
Abstract
In 2001, J. Hempel proved the existence of Heegaard splittings of arbitrarily high distance by using a high power of a pseudo-Anosov map as the gluing map between two handlebodies. We show that lower bounds on distance can also be obtained when using a high power of a suitably chosen Dehn twist. In certain cases, we can then determine the exact distance of the resulting splitting. These results can be seen as a natural extension of work by A. Casson and C. Gordon in 1987 regarding strongly irreducible Heegaard splittings.
Cite
@article{arxiv.1212.1199,
title = {High Distance Heegaard Splittings via Dehn Twists},
author = {Michael Yoshizawa},
journal= {arXiv preprint arXiv:1212.1199},
year = {2014}
}
Comments
26 pages, 13 figures