Graph manifolds with boundary are virtually special

Przytycki, Piotr; Wise, Daniel T.
June 2014
Journal of Topology;Jun2014, Vol. 7 Issue 2, p419
Academic Journal
Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in π1M, and that the double cosets for crossing surfaces are also separable. We deduce that if there is a ‘sufficient’ collection of surfaces in M, then π1M is virtually the fundamental group of a special non-positively curved cube complex. We provide a sufficient collection for graph manifolds with boundary, thus proving that their fundamental groups are virtually special, and hence linear.


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