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2011 Line arrangements and direct products of free groups
Kristopher Williams
Algebr. Geom. Topol. 11(1): 587-604 (2011). DOI: 10.2140/agt.2011.11.587

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.

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Kristopher Williams. "Line arrangements and direct products of free groups." Algebr. Geom. Topol. 11 (1) 587 - 604, 2011. https://doi.org/10.2140/agt.2011.11.587

Information

Received: 8 October 2010; Revised: 9 December 2010; Accepted: 22 December 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1213.52019
MathSciNet: MR2783239
Digital Object Identifier: 10.2140/agt.2011.11.587

Subjects:
Primary: 52C30
Secondary: 14F35, 32S22

Rights: Copyright © 2011 Mathematical Sciences Publishers

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