Line arrangements and direct sums of free groups

Details Line arrangements and direct sums of free groups Line arrangements and direct sums of free groups

2010-09-27

arxiv.org/abs/1009.5271v1

Mathematics

Algebraic Topology

15 pages, 4 figures

Scientific paper

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 sum of free groups, then the complements of the arrangements are homotopy equivalent. For any such arrangement, we construct another arrangement that is complexified-real, the intersection lattices of the arrangements are isomorphic, and the complements of the arrangements are diffeomorphic.

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