The boundary manifold of a complex line arrangement

Abstract

We study the topology of the boundary manifold of a line arrangement in CP^2, with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial Delta(G), and more generally, the twisted Alexander polynomial associated to the abelianization of G and an arbitrary complex representation. We give an explicit description of the unit ball in the Alexander norm, and use it to analyze certain Bieri-Neumann-Strebel invariants of G. From the Alexander polynomial, we also obtain a complete description of the first characteristic variety of G. Comparing this with the corresponding resonance variety of the cohomology ring of G enables us to characterize those arrangements for which the boundary manifold is formal.

This is the version published by Geometry & Topology Monographs on 22 February 2008

References in corpus (6)

• Geometry of cohomology support loci for local systems I
• Characteristic varieties of arrangements
• Chen Lie algebras
• Twisted Alexander polynomials and surjectivity of a group homomorphism
• Boundary manifolds of projective hypersurfaces
• Topological invariance of intersection lattices of arrangements in CP^2

Cited by in corpus (9)

• Hyperplane arrangements and Milnor fibrations
• Fundamental groups, Alexander invariants, and cohomology jumping loci
• Quasi-Kähler groups, 3-manifold groups, and formality
• Reidemeister Torsion, Peripheral Complex, and Alexander Polynomials of Hypersurface Complements
• Residually finite rationally $p$ groups
• Characteristic varieties of graph manifolds and quasi-projectivity of fundamental groups of algebraic links
• Remarks On the Topology of the Fano surface
• Cohomology jump loci of 3-manifolds
• The homology groups of finite cyclic covering of line arrangement complement