Kenji Kozai will be visiting from Berkeley this Thursday and Friday. Let me
know if you would like to join us for lunch on Thursday. Kenji will speak
in the topology seminar on Thursday:
Hyperbolic structures from Sol
Abstract: Thurston's hyperbolization theorem states that the mapping torus
of a surface homeomorphism is a hyperbolic 3-manifold if and only if the
homeomorphism is pseudo-Anosov. On the other hand, the stretch-squeeze
dynamics of the pseudo-Anosov define a natural (singular) Sol metric on the
mapping torus, where the singular locus is the orbit of the singular points
of the stable and unstable foliations. In the case where the surface is a
punctured torus, it is known from results of Hodgson and
Heusener-Porti-Suarez that the Sol structure can be obtained as a rescaled
limit of hyperbolic cone structures -- in other words, hyperbolic
structures can be regenerated from Sol. Using different methods, the result
is generalized to pseudo-Anosov maps on higher complexity surfaces, as long
as the invariant foliations of the pseudo-Anosov are orientable and the
first Betti number of the mapping torus is 1.
