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3:40 pm Wednesday, August 24, 2011 Virtual Topology Seminar: Projective Representations of the Mapping Class group of a surface with boundary coming from TQFTby Charlie Frohman (University of Iowa) in HB 355- For each odd prime p, and primitive 2pth root unity, there is a projective representation of the mapping class group of a torus of dimension 2, that comes from the projective action of the mapping class group of a one punctured torus ( aka the modular group) on a portion of the state space assigned to a once punctured torus. I will prove up to conjugacy, this family extends to a continuous family of representations of the modular group defined on the unit circle. This family includes a twisted version of the canonical representation of the modular group. This means that the dilation coefficient of pseudo-anosov mapping classes can be computed as a limit of quantum invariants of mapping tori. It also means that the hyperbolic volume should also be computable, though the connection is less direct. (Joint with Joanna Kania-Bartoszynska and Mike Fitzpatrick)
Submitted by shelly@rice.edu |