Graph manifolds with boundary are virtually special

Details Graph manifolds with boundary are virtually special Graph manifolds with boundary are virtually special

2011-10-16

arxiv.org/abs/1110.3513v1

Mathematics

Geometric Topology

26 pages, 9 figures

Scientific paper

Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in the fundamental group of M, and that the double cosets of crossing surfaces are also separable. We deduce that if there is a "sufficient" collection of surfaces in M, then the fundamental group of M is virtually the fundamental group of a "special" nonpositively curved cube complex. That is a complex that admits a local isometry into the Salvetti complex of a right-angled Artin group. We provide a sufficient collection for graph manifolds with boundary thus proving that their fundamental groups are virtually special, in particular linear.

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