Superrigidity In Infinite Dimension And Finite Rank Via Harmonic Maps

TL;DR

This paper establishes a superrigidity property for certain group actions on infinite-dimensional nonpositively curved spaces, extending classical rigidity results to new geometric contexts.

Contribution

It introduces a superrigidity theorem for actions of cocompact lattices in higher rank semisimple Lie groups on infinite-dimensional nonpositive curvature manifolds.

Findings

Proves superrigidity for infinite-dimensional Riemannian manifolds.

Extends rigidity results to finite telescopic dimension spaces.

Provides new insights into group actions in geometric analysis.

Abstract

We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and finite telescopic dimension.