Generalized μ-Invariants for Links and Hyperplane Arrangements

Abstract

We construct a family, HM(k)k⩾ 2, of oriented topological equivalence invariants, for projective configurations of complex hyperplanes with fixed combinatorial pattern. We construct a family, PM(k)k ⩾ 2, of concordance invariants, for classical links with a fixed number of components. The constructions are carried out in the same manner, using the existence of natural additional structures on the nilpotent quotients of the fundamental groups of the complements. We give the explicit computation of the primary and secondary HM and PM invariants. 2000 Mathematical Subject Classification: primary 57M25, 32S50; secondary 20F10, 20F12.