Tuesday, March 25
Moon Duchin, UC Davis
The divergence rate of geodesics can be suitably defined so that flat spaces have linear divergence and hyperbolic spaces have exponential divergence. Gromov expected (in print) that in nonpositive curvature, there would be a "gap" between these rates. Gersten constructed a CAT(0) example with intermediate divergence, and this behavior has also been identified in some three-manifold groups. I'll discuss joint work with Kasra Rafi showing quite explicitly that Teichmuller space and the mapping class group both have quadratic divergence.
Back to seminar home page.