Quasi-isometry and finite presentations of left cancellative monoids

Details Quasi-isometry and finite presentations of left cancellative monoids Quasi-isometry and finite presentations of left cancellative monoids

2012-04-11

arxiv.org/abs/1204.2384v1

Mathematics

Group Theory

13 pages

Scientific paper

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 characterisation of finite presentability for left cancellative monoids. We also give examples to show that this characterisation does not extend to monoids in general, and indeed that properties such as solvable word problem are not isometry invariants for general monoids.

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