Groups Acting on Semimetric Spaces and Quasi-isometries of Monoids
نویسنده
چکیده
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 Švarc-Milnor Lemma to this setting. Among the most natural examples of these spaces are finitely generated monoids and semigroups and their Cayley and Schützenberger graphs; we apply our results to show a number of important properties of monoids are quasi-isometry invariants.
منابع مشابه
Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings
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