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.
Citation
Michael Yoshizawa. "High distance Heegaard splittings via Dehn twists." Algebr. Geom. Topol. 14 (2) 979 - 1004, 2014. https://doi.org/10.2140/agt.2014.14.979
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