| 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 repertoir
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.
|