Cohomology of Hyperplane Complements with Group Ring Coefficients

The Cohomology of a Coxeter Group with Group Ring Coefficients

Vanishing results for the cohomology of complex toric hyperplane complements

Suppose R is the complement of an essential arrangement of toric hyperlanes in the complex torus (C∗)n and π = π1(R). We show that H∗(R;A) vanishes except in the top degree n when A is one of the following systems of local coefficients: (a) a system of nonresonant coefficients in a complex line bundle, (b) the von Neumann algebra Nπ, or (c) the group ring Zπ. In case (a) the dimension of Hn is ...

Cohomology of Coxeter groupswith group ring coefficients: II

The cohomology of a group G with coefficients in a left G–module M is denoted H .GIM /. We are primarily interested in the case where M is the group ring, ZG . Since ZG is a G–bimodule, H .GIZG/ inherits the structure of a right G– module. When G is discrete and acts properly and cocompactly on a contractible CW complex , there is a natural topological interpretation for this cohomology group:...

The Cohomology of Right Angled Artin Groups with Group Ring Coefficients

We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.

Complex Hyperbolic Hyperplane Complements

We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n−1)-submanifold S . The main result is that the fundamental group of M \S is relatively hyperbolic, relative to fundamental groups of the ends of M \S , and M \S admits a complete finite volume A -regular Riemannian metric of negative sectional curvature. It fo...