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arXiv · 1808.02722

Quasi-isometry of pairs: surfaces in graph manifolds

Hoang Thanh Nguyen
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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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Hoang Thanh Nguyen. 2018-08-08. Quasi-isometry of pairs: surfaces in graph manifolds. https://arxiv.org/abs/1808.02722

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