Volume 13 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
MSP Books and Monographs
Other MSP Publications

The boundary manifold of a complex line arrangement

Daniel C Cohen and Alexander I Suciu

Geometry & Topology Monographs 13 (2008) 105–146

DOI: 10.2140/gtm.2008.13.105

arXiv: math.GT/0607274


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


line arrangement, graph manifold, fundamental group, twisted Alexander polynomial, BNS invariant, cohomology ring, holonomy Lie algebra, characteristic variety, resonance variety, tangent cone, formality

Mathematical Subject Classification

Primary: 32S22

Secondary: 57M27


Received: 30 May 2006
Revised: 29 May 2007
Accepted: 30 May 2007
Published: 22 February 2008

Daniel C Cohen
Department of Mathematics
Louisiana State University
Baton Rouge LA 70803
Alexander I Suciu
Department of Mathematics
Northeastern University
Boston MA 02115