Let G be the fundamental group of a closed orientable surface of genus at least 2, and α an automorphism of G. In a celebrated result, Thurston showed that the mapping torus Gαℤ is hyperbolic if and only if no power of α preserves a non-trivial conjugacy class. In this talk, I will describe joint work with François Dahmani, where we show that if G is torsion-free hyperbolic, then Gαℤ is relatively hyperbolic with optimal parabolic subgroups.

This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.