Finitely summable Fredholm modules over higher rank groups and lattices

TL;DR

This paper classifies finitely summable Fredholm modules over higher rank groups and lattices, linking to advanced group properties and extending understanding of operator algebras in this context.

Contribution

It provides a complete classification of Fredholm modules over higher rank groups and lattices, building on recent generalizations of Kazhdan's property T.

Findings

Classification up to smooth homotopy achieved

Connections established with property T generalizations

Results depend on recent work by Bader, Furman, Gelander, and Monod

Abstract

We give a complete classification (up to smooth homotopy) of finitely summable Fredholm representations (Fredholm modules) over higher rank groups and lattices. Our results are a direct consequence of work of Bader, Furman, Gelander and Monod on generalisations of Kazhdan's property T for locally compact groups.