Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Groups acting on semimetric spaces and quasi-isometries of monoids


Authors: Robert Gray and Mark Kambites
Journal: Trans. Amer. Math. Soc. 365 (2013), 555-578
MSC (2010): Primary 20M05, 20M30, 05C20
Published electronically: September 24, 2012
MathSciNet review: 2995365
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20M05, 20M30, 05C20

Retrieve articles in all journals with MSC (2010): 20M05, 20M30, 05C20


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
Email: Mark.Kambites@manchester.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05868-5
Keywords: Monoid, group, finitely generated, action, semimetric space, quasimetric space
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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.