The boundary manifold of a complex line arrangement

Details The boundary manifold of a complex line arrangement The boundary manifold of a complex line arrangement

2006-07-12

arxiv.org/abs/math/0607274v3

Geom. Topol. Monogr. 13 (2008) 105-146

Mathematics

Geometric Topology

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

Scientific paper

10.2140/gtm.2008.13.105

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.

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