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.
This is a reminder for Kenji Kozai's talk on Thursday Apr 23, 3:30 in MSCS 514.
On Mon, Apr 20, 2015 at 4:11 PM Henry Segerman segerman@math.okstate.edu wrote:
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.
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Henry Segerman