Groups acting on semimetric spaces and quasi-isometries of monoids
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- by Robert Gray and Mark Kambites PDF
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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 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 that a number of important properties of monoids are quasi-isometry invariants.References
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Additional Information
- Robert Gray
- Affiliation: School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland
- Address at time of publication: CAUL Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
- Email: rdgray@fc.ul.pt
- Mark Kambites
- Affiliation: School of Mathematics, University of Manchester, Manchester M13 9PL, England
- MR Author ID: 760844
- Email: Mark.Kambites@manchester.ac.uk
- Received by editor(s): August 25, 2009
- Published electronically: September 24, 2012
- Additional Notes: The first author’s research was supported by an EPSRC Postdoctoral Fellowship.
The second author’s research was supported by an RCUK Academic Fellowship. The second author gratefully acknowledges the support of the Centre for Interdisciplinary Research in Computational Algebra during a visit to St Andrews. - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 555-578
- MSC (2010): Primary 20M05, 20M30, 05C20
- DOI: https://doi.org/10.1090/S0002-9947-2012-05868-5
- MathSciNet review: 2995365