Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 1 (2011), 587-604.
Line arrangements and direct products of free groups
We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct product of free groups, then the complements of the arrangements are homotopy equivalent. For any such arrangement , we also construct an arrangement such that is a complexified-real arrangement, the intersection lattices of the arrangements are isomorphic, and the complements of the arrangements are diffeomorphic.
Algebr. Geom. Topol., Volume 11, Number 1 (2011), 587-604.
Received: 8 October 2010
Revised: 9 December 2010
Accepted: 22 December 2010
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 52C30: Planar arrangements of lines and pseudolines
Secondary: 32S22: Relations with arrangements of hyperplanes [See also 52C35] 14F35: Homotopy theory; fundamental groups [See also 14H30]
Williams, Kristopher. Line arrangements and direct products of free groups. Algebr. Geom. Topol. 11 (2011), no. 1, 587--604. doi:10.2140/agt.2011.11.587. https://projecteuclid.org/euclid.agt/1513715195