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arXiv · 1212.1199

High Distance Heegaard Splittings via Dehn Twists

Michael Yoshizawa
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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.

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Michael Yoshizawa. 2012-12-05. High Distance Heegaard Splittings via Dehn Twists. https://doi.org/10.2140/agt.2014.14.979

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