Quasi-isometry of pairs: surfaces in graph manifolds
Abstract
We show there exists a closed graph manifold N and infinitely many non-separable, horizontal surfaces \Sn N\n ∈ N such that there does not exist a quasi-isometry π1(N) π1(N) taking π1(Sn) to π1(Sm) within a finite Hausdorff distance when n ≠ m.
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