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

2015/12/24 by Lavy, Omer
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/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 St_n(F_p⟨ t₁,… ,t_k ⟩) on Hadamard manifold when n ≥ 3 is finite. We further study actions on infinite dimensional manifolds and prove a fixed point theorem related to such actions.

Related

• Fixed point properties of nilpotent and solvable Lie group actions on\n Hadamard manifolds
• The geodesic flow of a nonpositively curved graph manifold
• Almost isometric actions, property (T), and local rigidity
• Borel actions in nonpositively curved geometry and the Nielsen realisation problem
• Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds