Line arrangements and direct products of free groups

Williams, Kristopher¹

¹Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City 52242, USA

Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 587-604

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.587

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

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