03/29: Barbara Schapira

Critical exponents and amenability of covers

Abstract: In this joint work with R Coulon, R Dougall and S Tapie, we prove the following result. Let $\Gamma'<\Gamma$ be two discrete groups acting properly isometrically on a hyperbolic space $X$ . Then their critical exponents coincide if and only if the small group $\Gamma'$ is coamenable in $\Gamma$ . In this talk, I will explain the statement and sketch the main steps of the proof, which involves a strange construction of so-called twisted Patterson-Sullivan measures.

Slides