Joint OU-OSU Geometry and Topology Seminar
Applications of tropical geometry to groups and manifolds
Stephan Tillmann, University of Melbourne
Details
Wednesday April 9, 2008
809 Physical Sciences Center
4:00 pm / 3:30 tea
Abstract
The interplay between valuations associated to ideal points of character varieties and length functions for actions on trees has been used successfully to prove many deep results concerning the topology and geometry of 3-manifolds. Constructions due to Culler, Morgan and Shalen have formalised this relationship and form part of the standard repertoire in the field. I will motivate and describe a combinatorial and geometric variant of their constructions using hyperbolic and tropical geometry which leads to new algorithms in the study of 3-manifolds. If time permits, I will also talk about related concepts in the study of finitely generated groups linking the Bieri-Neumann-Strebel invariant to tropical geometry.