pdcarrasco - Thermodynamic Formalism for Quasimorphisms: Lattices in

Journal article

Pablo D. Carrasco, Federico Rodríguez-Hertz

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Carrasco, P. D., & Rodríguez-Hertz, F. Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups.

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

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Carrasco, Pablo D., and Federico Rodríguez-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 Rodríguez-Hertz, Federico}
}

We give a proof, based on thermodynamic formalism, of a theorem in bounded cohomology extending a foundational result of Burger and Monod: if $\Gamma$ is an irreducible uniform lattice in a non-compact connected semisimple Lie group of real rank at least $2$, then for any finite-dimensional representation $\pi:\Gamma\to \On_N$, every $\pi$-quasimorphism (that is, a map with bounded defect with respect to $\pi$) is bounded.