Alexander Invariants of Complex Hyperplane Arrangements

Abstract

Let A be an arrangement of complex hyperplanes. The fundamental group of the complement of A is determined by a braid monodromy homomorphism from a finitely generated free group to the pure braid group. Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of A. From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of A. We also provide a combinatorial criterion for when these lower bounds are attained.

26 pages; LaTeX2e with amscd, amssymb packages

Cited by in corpus (7)

• Translated tori in the characteristic varieties of complex hyperplane arrangements
• Boundary manifolds of projective hypersurfaces
• Chen ranks and resonance
• The pure braid groups and their relatives
• Pure virtual braids, resonance, and formality
• Homology, lower central series, and hyperplane arrangements
• Alexander invariants and cohomology jump loci in group extensions