Line arrangements and direct products of free groups

Williams, Kristopher

doi:10.2140/agt.2011.11.587

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Line arrangements and direct products of free groups

Kristopher Williams

Algebraic & Geometric Topology 11 (2011) 587–604

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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 52C30

Secondary: 32S22, 14F35

References

Publication

Received: 8 October 2010

Revised: 9 December 2010

Accepted: 22 December 2010

Published: 19 February 2011

Authors

Kristopher Williams
Department of Mathematics University of Iowa 14 MacLean Hall Iowa City 52242 USA
http://math.uiowa.edu/~kjwillia

Volume 11, issue 1 (2011)