Character varieties and essential surfaces in arbitrary characteristic
Grace Garden (Jussieu-Paris)
Abstract: In the seminal work of Culler and Shalen (1983) a method is outlined
to detect essential surfaces in a three-manifold by studying their
SL(2,C)-character variety. The method underscores connections between
the theory of incompressible surfaces in three-manifolds, splittings
of fundamental groups, group actions on trees, and the geometry of
representation varieties. In this talk, we will motivate and then lay
a general foundation for this theory in arbitrary characteristic by
using the same approach instead over F, an algebraically closed field
of positive characteristic. We then apply the theory to a variety of
settings. This is joint work with Stephan Tillmann.