Contracting Automorphisms and L-cohomology in Degree One
نویسندگان
چکیده
We characterize those Lie groups (as well as algebraic groups over a local field of characteristic zero) whose first reduced L-cohomology is zero for all p > 1, extending a result of Pansu. As an application, we obtain a description of Gromov-hyperbolic groups among those groups. In particular we prove that any non-elementary Gromov-hyperbolic algebraic group over a non-Archimedean local field of zero characteristic is quasi-isometric to a 3regular tree. We also extend the study to semidirect products of a general locally compact group by a cyclic group acting by contracting automorphisms.
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