Mathematics Colloquia and Seminars

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Description

In 1995 Casson outlined a program to try to prove hyperbolic structures exist on irreducible atoroidal 3-manifolds with tori boundary. So the aim is to give an `elementary' proof of geometrisation in this case. The idea was to solve Thurston's gluing equations starting with a good ideal triangulation. Casson has written a computer program which works extrmely well but has not been able to make further progress on this. I will talk about joint work with Ensil Kang from Chosun University. We have been able to show that Lackenby's taut ideal triangulations ( Geometry and Topology 2000) can be deformed to angle structures if and only if a certain interesting combinatorial obstruction vanishes. For the simple case of once punctured torus bundles over the circle, with pseudo Anosov gluing, we are able to show this obstruction vanishes if and only if the simplest layered triangulation is picked.