Fixed point theorems for groups acting on non-positively curved manifolds

Omer Lavy

paper

Fixed point theorems for groups acting on non-positively curved manifolds

arXiv:1512.07745

Abstract

We study isometric actions of Steinberg groups on Hadamard manifolds. We prove some rigidity properties related to these actions. In Particular we show that every isometric action of $S t_{n} (F_{p} ⟨ t_{1}, \dots, t_{k} ⟩)$ on Hadamard manifold when $n \geq 3$ is finite. We further study actions on infinite dimensional manifolds and prove a fixed point theorem related to such actions.