Hokkaido Mathematical Journal

KAWAHARA Yukihito,

The twisted de Rham cohomology for basic constructionsof hyperplane arrangements and its applications.

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
MSC(Secondary)14F40, 32S22
Uncontrolled Keywordstwisted de Rham cohomology, hyperplane arrangement