Quasi-isometry and finite presentations of left cancellative monoids
Rob Gray,Mark Kambites +1 more
TLDR
It is shown that being finitely presentable and being finally presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids.Abstract:
We show that being finitely presentable and being finitely presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids. Our main tool is an elementary, but useful, geometric characterization of finite presentability for left cancellative monoids. We also give examples to show that this characterization does not extend to monoids in general, and indeed that properties such as solvable word problem are not isometry invariants for general monoids.read more
Citations
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Amenability and geometry of semigroups
Rob Gray,Mark Kambites +1 more
TL;DR: In this article, the connection between amenability, Folner conditions and the geometry of finitely generated semigroups was studied, and it was shown that left amenability coincides with the strong Folner condition.
Journal ArticleDOI
A strong geometric hyperbolicity property for directed graphs and monoids
Rob Gray,Mark Kambites +1 more
TL;DR: In this paper, it was shown that finitely generated left cancellative monoids whose right Cayley graphs satisfy this condition must be finitely presented with polynomial Dehn functions, and hence word problems in NP.
Posted Content
Amenability and geometry of semigroups
Rob Gray,Mark Kambites +1 more
TL;DR: The connection between amenability and the geometry of finitely generated semigroups was studied in this paper, where it was shown that left amenability coincides with the strong F{o}lner condition.
Posted Content
Finite presentability and isomorphism of Cayley graphs of monoids
TL;DR: In this article, two finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabeled) Cayley graphs are isomorphic, and they are shown to be isomorphic.
Dissertation
Dots and lines : geometric semigroup theory and finite presentability
TL;DR: In this article, it was shown that finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not a property under quasi-isometry of Cayley graphs.
References
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Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
Patrick Dehornoy,Luis Paris +1 more
TL;DR: In this article, it was shown that Garside groups are geodesically fully biautomatic, and that the language of normal forms for Gaussian groups is regular, symmetric, and geodesic.
Journal ArticleDOI
Quasi-actions on trees I. Bounded valence
TL;DR: In this paper, it was shown that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T'.
Book
A Course On Geometric Group Theory
TL;DR: These notes are based on a series of lectures I gave at the Tokyo Institute of Technology from April to July 2005, which constituted a course entitled “An introduction to geometric group theory” totalling about 20 hours, and attempt to present a logically coherent introduction to the subject.