Gromov boundary of the Grand Arc graph

Carolyn Abbott; Assaf Bar-Natan; Arya Vadnere

Gromov boundary of the Grand Arc graph

Geometric Topology 2026-07-01 v1

Authors: Carolyn Abbott , Assaf Bar-Natan , Arya Vadnere

Abstract

We describe a dense subset of the Gromov boundary of the grand arc graph of an infinite-type surface as a space of geodesic laminations, analogous to Klarreich's description of the Gromov boundary of the curve complex. After showing that the grand arc graph satisfies a bounded geodesic image theorem, we also prove that the boundary is not compact.

Keywords

grand arc graph Gromov boundary geodesic laminations curve complex infinite-type surface

Cite

@article{arxiv.2607.00957,
  title  = {Gromov boundary of the Grand Arc graph},
  author = {Carolyn Abbott and Assaf Bar-Natan and Arya Vadnere},
  journal= {arXiv preprint arXiv:2607.00957},
  year   = {2026}
}

Comments

54 pages, 15 figures