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High Distance Heegaard Splittings via Dehn Twists
Geometry/Topology| Speaker: | Michael Yoshizawa |
| Location: | 2112 MSB |
| Start time: | Tue, Nov 13 2012, 3:10PM |
Description
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.