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arXiv · 2603.28535

Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups

Pablo D. Carrasco·Federico Rodriguez-Hertz
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Abstract

We give a new proof, based on thermodynamic formalism, of a foundational result of Burger and Monod in bounded cohomology. Let $G$ be a noncompact connected semisimple real Lie group with finite center and no factors of real rank one, and let $Γ<G$ be a uniform lattice. We prove that, for every orthogonal representation $π:Γ\to\operatorname{O}_N$, every $π$-quasimorphism $L:Γ\to\mathbb{R}^N$ is bounded.

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Pablo D. Carrasco, Federico Rodriguez-Hertz. 2026-09-09. Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups. https://arxiv.org/abs/2603.28535

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