Quasi-isometry of pairs: surfaces in graph manifolds

2018/08/08 by Nguyen, Hoang Thanh
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1808.02722

Abstract

We show there exists a closed graph manifold N and infinitely many non-separable, horizontal surfaces \S_n → N\_{n ∈ ℕ} such that there does not exist a quasi-isometry π₁(N) → π₁(N) taking π₁(S_n) to π₁(S_m) within a finite Hausdorff distance when n ≠ m.

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