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Automatic Structures for Torus Link Groups

Matthieu Picantin

Laboratoire de Mathématiques, Nicolas Oresme CNRS UMR 6139, Université de Caen BP 5186 F-14032 Caen, France

https://doi.org/10.1142/S0218216503002627Cited by:12 (Source: Crossref)

Abstract

A general result of Epstein and Thurston implies that all link groups are automatic, but the proof provides no explicit automaton. Here we show that the groups of all torus links are groups of fractions of so-called Garside monoids, i.e., roughly speaking, monoids with a good theory of divisibility, which allows us to reprove that those groups are automatic, but, in addition, gives a completely explicit description of the involved automata, thus partially answering a question of D. F. Holt.

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