On the coarse-geometric detection of subgroups

Details On the coarse-geometric detection of subgroups On the coarse-geometric detection of subgroups

2010-06-10

arxiv.org/abs/1006.2114v1

Mathematics

Group Theory

39 pages, no figures

Scientific paper

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.

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