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Taut and Angle structures for ideal triangulations of 3-manifoldsGeometry/Topology
|Speaker: ||J. Hyam Rubinstein, Melbourne University, Australia|
|Location: ||693 Kerr|
|Start time: ||Wed, Feb 2 2005, 4:10PM|
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.