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### Natural Volumes on Character Varieties and the Turaev-Viro invariant at level Infinity

**Geometry/Topology**

Speaker: | Charlie Frohman, University of Iowa |

Location: | 693 Kerr |

Start time: | Wed, Feb 4 2004, 3:10PM |

If M is an oriented homology three sphere so that every representation rho: pi_1(M) --> SU(2) satisfies strong rigidity, then there is an invariant volume on the character variety of M that is defined via a Heegaard splitting. After reviewing the definition of the volume we compute the total volume of the character variety. The total volume is the heat kernel regularization of the divergent formula for the Turaev-Viro invariant of M at level infinity.