Cohomology computations of solvmanifolds with local coefficients

2012/08/20 by Hisashi Kasuya, Kasuya, Hisashi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Group Theory (math.GR) #K-Theory and Homology (math.KT) #math.GR #math.GT #math.KT

paper · pdf · doi:10.48550/arxiv.1208.4045

This paper has been withdrawn by the author.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

openalex publication_date 2012/08/20 · arxiv created 2013/11/09 · arxiv updated 2013/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a simply connected solvable Lie group with a lattice Γ and N the nilradical of G. For a complex valued representation ρ: G→ GL(V_ρ) such that the restriction ρ_|_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/Γ with twisted by ρ.

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