pdcarrasco - Thermodynamic Formalism for Quasimorphisms: Lattices in

Journal article

Pablo D. Carrasco, Federico Rodriguez-Hertz

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APA Click to copy
Carrasco, P. D., & Rodriguez-Hertz, F. Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups.

Chicago/Turabian Click to copy
Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups” (n.d.).

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Carrasco, Pablo D., and Federico Rodriguez-Hertz. Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups.

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@article{pablo-a,
  title = {Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups},
  author = {Carrasco, Pablo D. and Rodriguez-Hertz, Federico}
}

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 $\Gamma<G$ be a uniform lattice. We prove that, for every orthogonal representation $\pi:\Gamma\to\On_N$, every $\pi$-quasimorphism $L:\Gamma\to\R^N$ is bounded.