High distance Heegaard splittings via Dehn twists

Yoshizawa, Michael¹

¹Department of Mathematics, University of California, Santa Barbara, South Hall, Room 6607, Santa Barbara, CA 93106-3080, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 2, pp. 979-1004

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.979

Classification : 57M50, 57M25
Keywords: Heegaard splittings, Hempel distance

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