Graph manifolds with boundary are virtually special

By Piotr Przytycki, Daniel T. Wise. 2011

78 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/54847a9aaefbed8cca87d6c77e6b54e1a78e091c

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Hierarchically hyperbolic spaces II: Combination theorems and the distance formula (2015, background): “pactly, on a CAT(0) cube complex X, and the quotient is virtually special; this is a result of Liu [Liu13] which was also shown to hold in the case where M has nonempty boundary by Przytycki and Wise [PW14]. Moreover, ˇ 1Macts with nitely many orbits of hyperplanes. Hence the ˇ 1M{invariant factor s”
The Thurston norm and twisted Alexander polynomials (2012, methodology): “For such graph manifolds the theorem was also proved by Przytycki–Wise [38].”