Groups acting on semimetric spaces and quasi-isometries of monoids

Details Groups acting on semimetric spaces and quasi-isometries of monoids Groups acting on semimetric spaces and quasi-isometries of monoids

2009-06-02

arxiv.org/abs/0906.0473v1

Mathematics

Group Theory

25 pages

Scientific paper

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.

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