Groups acting on semimetric spaces and quasi-isometries of monoids
Group Theory
2009-06-03 v1
Abstract
We study groups acting by length-preserving transformations on spaces equipped with asymmetric, partially-defined distance functions. We introduce a natural notion of quasi-isometry for such spaces and exhibit an extension of the Svarc-Milnor Lemma to this setting. Among the most natural examples of these spaces are finitely generated monoids and semigroups and their Cayley and Schutzenberger graphs; we apply our results to show a number of important properties of monoids are quasi-isometry invariants.
Keywords
Cite
@article{arxiv.0906.0473,
title = {Groups acting on semimetric spaces and quasi-isometries of monoids},
author = {Robert Gray and Mark Kambites},
journal= {arXiv preprint arXiv:0906.0473},
year = {2009}
}
Comments
25 pages