Geometry and Analysis on Groups Research Seminar

"Geometry and Analysis on Groups" Research Seminar

Time: 2018.01.16, 15:15–17:00
Location: Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Critical exponents for normal subgroups."
Speaker: Rhiannon Dougall (Université de Nantes)
Abstract: Fix a cocompact group \(\Gamma_0\) of isometries of a negatively curved, simply connected manifold \(X\). We are interested in the dynamics of its normal subgroups \(\Gamma\). Namely, we study the critical exponent \(\delta_\Gamma\), which is the exponential growth rate of the \(\Gamma\)–orbit of a point. We characterise the existence of a gap \(\delta_\Gamma<\delta_{\Gamma_0}\) uniform in a family of normal subgroups \(\Gamma\), in terms of permutation representations given by the quotients \(\Gamma_0/\Gamma\). The proof uses the symbolic dynamics for the geodesic flow, for which we obtain the analogous statements for countable state shifts obtained as group extensions of a finite state shift.