** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2018.10.09, 15:00–17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Cogrowth for group actions with a
strongly contracting element."

**Speaker:** Christopher
Cashen (Universität Wien)

**Abstract:**
We show that for a finitely generated group \(G\) acting properly on a geodesic metric space \(X\) with a strongly contracting element and purely exponential growth, and for every infinite normal subgroup \(N\) of \(G\), the growth rates \(\delta_G\) and \(\delta_N\) of the orbits of \(G\) and \(N\) in \(X\) satisfy \(\delta_N/\delta_G > 1/2\). This generalizes several results where the same conclusion is obtained for \(G\) a free group or \(X\) a negatively curved space.
This is joint work with Arzhantseva.