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

**Title:**
Small C ^ 1 actions of semidirect products on compact manifolds.

**Speaker:**
Sang-hyun Kim (KIAS)

**Abstract:**
For a compact Riemannian manifold \(M\) and for a finitely generated group \(G = H \rtimes\langle t\rangle\) with a hyperbolic linear action of \(t\) on \(H^1(H, \mathbb{Z})\), every \(C^1\)--action of \(G\) on \(M\) that is sufficiently close to the trivial action has an abelian image. As an example, we deduce the same conclusion when \(G\) is a fibered 3-manifold group. This is a joint work with Chritian Bonatti, Thomas Koberda and Michele Triestino.