‘Hyperbolicity of monoids presented by confluent monadic rewriting systems’
Beiträge zur Algebra und Geometrie, 54, no. 2 (October 2013), pp. 593–608.
DOI: 10.1007/s13366-012-0116-4. MR: 3095744. ZBL: 1326.20056.

Abstract

The geometry of the Cayley graphs of monoids defined by regular confluent monadic rewriting systems is studied. Using geometric and combinatorial arguments, these Cayley graphs are proved to be hyperbolic, and the monoids to be word-hyperbolic in the Duncan–Gilman sense. The hyperbolic boundary of the Cayley graph is described in the case of finite confluent monadic rewriting systems.