Quasi-isometry of pairs: surfaces in graph manifolds
classification
🧮 math.GR
keywords
graphquasi-isometrysurfacestherecloseddistanceexistexists
read the original abstract
We show there exists a closed graph manifold $N$ and infinitely many non-separable, horizontal surfaces $\{S_{n} \to N\}_{n \in \mathbb{N}}$ such that there does not exist a quasi-isometry $\pi_1(N) \to \pi_1(N)$ taking $\pi_1(S_{n})$ to $\pi_1(S_{m})$ within a finite Hausdorff distance when $n \neq m$.
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