High distance Heegaard splittings via Dehn twists

Yoshizawa, Michael

doi:10.2140/agt.2014.14.979

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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

Volume 14, issue 2 (2014)