Groups acting on semimetric spaces and quasi-isometries of monoids

Mark Kambites (University of Manchester)

Wednesday 27th January, 2010 16:00-17:00 204


I shall describe recent joint work with Robert Gray on the development of geometric methods for finitely generated monoids and semigroups. We study a natural notion of quasi-isometry between spaces equipped with asymmetric, partially defined distance functions, and hence between finitely generated semigroups and monoids. It transpires that, just as for groups, many natural algebraic and geometric properties of monoids and semigroups are quasi-isometry invariants. A key tool is an extension of the Svarc-Milnor Lemma to the setting of groups acting by length-preserving transformations on asymmetric distance spaces.

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