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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