an:06673333
Zbl 1401.20035
Kasuya, Hisashi
Central theorems for cohomologies of certain solvable groups
EN
Trans. Am. Math. Soc. 369, No. 4, 2879-2896 (2017).
00362178
2017
j
20F16 20G10 20J06 22E41 22E25 17B56 57T15
group cohomology of torsion-free virtually polycyclic group; continuous cohomology of simply connected solvable Lie group; rational cohomology of algebraic group; de Rham cohomology of solvmanifold
Summary: We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are generalizations of certain results on the cohomology of solvmanifolds and infra-solvmanifolds. Moreover as an application of our results, we give a new proof of the surprising cohomology vanishing theorem given by \textit{K. Dekimpe} and \textit{P. Igodt} [Invent. Math. 129, No. 1, 121--140 (1997; Zbl 0867.20031)].
Zbl 0867.20031