The lecture describes some recent work that aims to generalize a well-known L.C.S. formula for the fundamental group of hyperplane arrangement complement. The main object of interest here is a “homotopy Lie algebra” which arises in commutative algebra and rational homotopy theory. It is shown that one can describe the algebra explicitly in terms of combinatorial ingredients in certain cases. Finally, some applications are given.

Keywords:

Arrangements of hyperplanes;quadratic duality; hypersolvable arrangements.

Lecture #10654

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