The subword reversing method

Patrick Dehornoy (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We summarize the main known results involving subword reversing, a method of semigroup theory for constructing van Kampen diagrams by referring to a preferred direction. In good cases, the method provides a powerful tool for investigating presented (semi)groups. In particular, it leads to cancellativity and embeddability criteria for monoids and to efficient solutions for the word problem of monoids and groups of fractions.

Mots clés: semigroup presentation; van Kampen diagram; rewrite system; cancellativity; word problem; Garside monoid; group of fractions; monoid embeddability

Domaines: Théorie des groupes [math.GR]

Patrick Dehornoy. The subword reversing method. 2009. ⟨hal-00442274⟩