Elsevier

Topology

Volume 42, Issue 1, January 2003, Pages 265-289
Topology

π1-classification of real arrangements with up to eight lines

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Abstract

One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups.

MSC

primary 14H30
secondary 52C30

Keywords

Line arrangement
Fundamental group
Incidence lattice
Classification

Cited by (0)

1

Partially supported by The Israel Science Foundation (Center of Excellence Program), and by the Emmy Noether Institute for Mathematics and by the Minerva Foundation (Germany). The research was done during the Ph.D. studies of David Garber, under the supervision of Prof. Mina Teicher.

2

Partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Subjects.