  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.
