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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.28535 |
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| _version_ | 1866914431762432000 |
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| author | Carrasco, Pablo D. Rodriguez-Hertz, Federico |
| author_facet | Carrasco, Pablo D. Rodriguez-Hertz, Federico |
| contents | We give a proof, based on thermodynamic formalism, of a theorem in bounded cohomology extending a foundational result of Burger and Monod: if $Γ$ 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 $π:Γ\to \operatorname{O}_N$, every $π$-quasimorphism (that is, a map with bounded defect with respect to $π$) is bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28535 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups Carrasco, Pablo D. Rodriguez-Hertz, Federico Dynamical Systems Geometric Topology 37D35 (Primary), 20F67 We give a proof, based on thermodynamic formalism, of a theorem in bounded cohomology extending a foundational result of Burger and Monod: if $Γ$ 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 $π:Γ\to \operatorname{O}_N$, every $π$-quasimorphism (that is, a map with bounded defect with respect to $π$) is bounded. |
| title | Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups |
| topic | Dynamical Systems Geometric Topology 37D35 (Primary), 20F67 |
| url | https://arxiv.org/abs/2603.28535 |