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High Distance Heegaard Splittings via Dehn Twists


Speaker: Michael Yoshizawa
Location: 2112 MSB
Start time: Tue, Nov 13 2012, 3:10PM

In 2001, J. Hempel found examples of Heegaard splittings of arbitrarily high distance by starting with the double of a handlebody H and then applying a high power of a pseudo-Anosov map on the boundary of H. We show that lower bounds on distance can also be obtained when using a high power of a suitable Dehn twist. In certain cases, this lower bound allows us to determine the exact distance of the resulting splitting. This is one of the first explicit constructions of Heegaard splittings of high distance whose exact distance can be determined.