Central theorems for cohomologies of certain solvable groups
Group Theory
2015-09-30 v4 Algebraic Geometry
Geometric Topology
K-Theory and Homology
Representation Theory
Abstract
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 certian results on the cohomology of solvmanifolds and infra-solvmanifolds. Moreover as an application of our results, we give a simple proof of the surprising cohomology vanishing theorem given by Dekimpe-Igodt.
Cite
@article{arxiv.1311.1310,
title = {Central theorems for cohomologies of certain solvable groups},
author = {Hisashi Kasuya},
journal= {arXiv preprint arXiv:1311.1310},
year = {2015}
}
Comments
To appear in Transactions of the AMS