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High distance Heegaard splittings via Dehn twists

Michael Yoshizawa
Algebraic & Geometric Topology 14 (2014) 979–1004
DOI: 10.2140/agt.2014.14.979
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.

Keywords
Heegaard splittings, Hempel distance
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57M25
References
Publication
Received: 9 December 2012
Revised: 25 September 2013
Accepted: 26 September 2013
Published: 21 March 2014
Authors
Michael Yoshizawa
Department of Mathematics
University of California, Santa Barbara
South Hall, Room 6607
Santa Barbara, CA 93106-3080
USA
http://math.ucsb.edu/~myoshi