We study the topology of the boundary manifold of a line arrangement
in CP2, with emphasis on the fundamental group G and
associated invariants. We determine the Alexander polynomial Δ(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.
For Fred Cohen on the occasion of his
sixtieth birthday
Keywords
line arrangement, graph manifold,
fundamental group, twisted Alexander polynomial, BNS
invariant, cohomology ring, holonomy Lie algebra,
characteristic variety, resonance variety, tangent cone,
formality
