Dynamical Resistance Day

Amenability of covers of negatively curved manifolds
26 de Junho | 11h00min | Barbara Schapira (Univ. Rennes 1, France)

Title: Amenability of covers of negatively curved manifolds (video)

Let M be a negatively curved manifold. If M is “strongly positively recurrent”, i.e. there is a critical gap between its entropy at infinity and its entropy, we show that a cover M' of M is amenable if and only if the critical exponents of M' and M coincide. The proof uses a construction of Patterson-Sullivan measures twisted by a representation. During the talk, I will explain this statement and present the main lines of the proof. This is a joint work with R. Dougall, R. Coulon and S.Tapie.