The lecture begins with three equivalent definitions of a local system on the complement of an arrangement. Then homology of the complement with coefficients in the local system is defined, and theorem of Hattori concerning the local system homology of a general position arrangement is stated. Features of Hattori's complex, and similar complexes arising in the context of super solvable arrangements are discussed. The lecture concludes with a discussion of the relationship between the cohomology of the Orik-Solomon algebra and the local system cohomology of the complement.

Keywords:

Arrangements of hyperplanes; local systems; flat connection; Orlik-Solomon algebra representation of the fundamental group; vanishing theorems.

Lecture #10648

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