# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 34 (2005) pp.489-505

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### Abstract

In this paper we study the twisted de Rham cohomology for an arrangement of hyperplanes. We prove formulas for basic constructions of arrangements: the twisted K\"{u}nneth formula for products or decompositions, the long exact sequence for triple constructions, and the relation for coning and deconing constructions. Moreover, we obtain the vanishing, dimension, and basis of the twisted de Rham cohomology for an arrangement in general position and a generic arrangement with arbitrary weight.

MSC(Primary) 55N25 14F40, 32S22 twisted de Rham cohomology, hyperplane arrangement