Algebraic & Geometric Topology

Line arrangements and direct products of free groups

Kristopher Williams

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Abstract

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 A, we also construct an arrangement A such that A is a complexified-real arrangement, the intersection lattices of the arrangements are isomorphic, and the complements of the arrangements are diffeomorphic.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 1 (2011), 587-604.

Dates
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
https://projecteuclid.org/euclid.agt/1513715195

Digital Object Identifier
doi:10.2140/agt.2011.11.587

Mathematical Reviews number (MathSciNet)
MR2783239

Zentralblatt MATH identifier
1213.52019

Subjects
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]

Keywords
line arrangement fundamental group hyperplane arrangement direct product of free groups homotopy type

Citation

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


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