Higher property T and below-rank phenomena of lattices (2511.20192v1)

Published 25 Nov 2025 in math.GR, math.GT, and math.OA

Abstract: The purpose of this paper is twofold. We explore higher property T as an abstract group-theoretic property. In particular, we provide new operator-algebraic characterizations of higher property T. Then we turn to lattices in semisimple Lie groups. We relate higher property T to other cohomological, rigidity and geometric phenomena below the real rank. The second part outlines a conjectural framework that unifies these aspects and reviews recent advances.

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