Graph manifolds with boundary are virtually special
نویسندگان
چکیده
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.
منابع مشابه
Mixed 3–manifolds Are Virtually Special
LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that π1M is virtually special.
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