7 mar 2016 -- 14:30
Aula Tricerri, DiMaI, Firenze
Abstract.
Solvmanifolds (resp. nilmanifolds) are quotients of simply connected solvable (resp. nilpotent) Lie groups by cocompact discrete subgroups. In 1950s, K. Nomizu proved that the de Rham cohomology of nilmanifolds are computed by the invariant differential forms. This theorem was generalized for “special” solvmanifolds by A. Hattori and G. D. Mostow. But, we can not obtain a "simple" generalization of Nomizu's Theorem for general solvmanifolds. In this talk, we give techniques of computations of the de Rham cohomology of general solvmanifolds and we give simplicial rational extended Nomizu's Theorem.