Geometry, Topology and Dynamics Seminar
David Futer
Michigan State University
Geometry and combinatorics of arborescent link complements
Abstract: We study the geometry and combinatorics of arborescent
links by cutting up their complements into angled ideal tetrahedra.
The vertices of these tetrahedra lie "at infinity," i.e. on the knot,
and the edges are assigned dihedral angles that fit together nicely
in the gluing. Such an angled triangulation does not quite give us a
hyperbolic structure on the knot complement, but it does tell us
exactly when a hyperbolic structure exists (reproving an old theorem
of Bonahon and Siebenmann). It also gives a lot of control over
surfaces in the link complement, and can hopefully lead to volume
estimates. This is joint work with François Guéritaud.
Monday April 24, 2006 at 3:00 PM in SEO 512