Algebraic & Geometric Topology 5 (2005) 691–711

DOI: 10.2140/agt.2005.5.691

arXiv: math.AT/0410363

Abstract

For line arrangements in P² with nice combinatorics (in particular, for those which are nodal away the line at infinity), we prove that the combinatorics contains the same information as the fundamental group together with the meridianal basis of the abelianization. We consider higher dimensional analogs of the above situation. For these analogs, we give purely combinatorial complete descriptions of the following topological invariants (over an arbitrary field): the twisted homology of the complement, with arbitrary rank one coefficients; the homology of the associated Milnor fiber and Alexander cover, including monodromy actions; the coinvariants of the first higher non-trivial homotopy group of the Alexander cover, with the induced monodromy action.

Keywords

hyperplane arrangement, oriented topological type, 1–marked group, intersection lattice, local system, Milnor fiber, Alexander cover

Mathematical Subject Classification

Primary: 32S22, 55N25

Secondary: 14F35, 52C35, 55Q52

References

Forward citations

Publication

Received: 18 October 2004
Revised: 12 May 2005
Accepted: 27 June 2005
Published: 5 July 2005

Authors