English

On the coarse-geometric detection of subgroups

Group Theory 2010-06-11 v1

Abstract

We generalize [Vav] to give sufficient conditions, primarily on coarse geometry, to ensure that a subset of a Cayley graph is a finite Hausdorff distance from a subgroup. Using this result, we prove a partial converse to the Flat Torus Theorem for CAT(0) groups. Also using this result, we give sufficient conditions for subgroups and splittings to be invariant under quasi-isometries.

Keywords

Cite

@article{arxiv.1006.2114,
  title  = {On the coarse-geometric detection of subgroups},
  author = {Diane M. Vavrichek},
  journal= {arXiv preprint arXiv:1006.2114},
  year   = {2010}
}

Comments

39 pages, no figures

R2 v1 2026-06-21T15:34:36.765Z