## Topology & Geometric Group Theory Seminar

## Fall 2008

### 1:30 – 2:30, Malott 406

Tuesday, December 2

**Helen
Wong**, Bowdoin College

*The mapping class group, Heegaard splittings, and quantum
invariants for 3-manifolds*

Under the umbrella of the Witten-Reshetikhin-Turaev topological
quantum field theory, we find projective unitary representations of
the mapping class group, 3-manifold invariants, and a slew of
applications to low-dimensional topology. In particular, the quantum
theory provides a set of lower bounds for the Heegaard genus of a
3-manifold. We give specific Seifert-fibred examples where the
quantum lower bounds are sharp and moreover are better than the rank
of the fundamental group. In joint work with Nathan Dunfield, we
study the effectiveness of the quantum lower bounds generically, i.e.,
for a `random Heegaard splitting' obtained from a random walk on the
mapping class group.

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