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.