Cohomology computations of solvmanifolds with local coefficients

Abstract

Let $G$ be a simply connected solvable Lie group with a lattice $\Gamma$ and $N$ the nilradical of $G$. For a complex valued representation $\rho :G\to GL(V_{\rho })$ such that the restriction ${\rho }_{{|}_N}$ is unipotent, as an advanced variation of cohomology computation of solvmanifolds by using Lie algebra cohomology, we construct a explicit finite dimensional cochain complex whose cohomology is isomorphic to the cohomology of $G/\Gamma$ with twisted by $\rho$.

arXiv commentThis paper has been withdrawn by the author. The results in this paper included in arXiv:1207.3988