Rub'en Blasco-Garc'ia, Mar'ia Cumplido, Derek F. Holt, Rose Morris-Wright, Sarah Rees
Published 2024-12-14Version 1
We prove that the word problem in an Artin group G based on a diagram without A_3 or B_3 subdiagrams can be solved using a system of length preserving rewrite rules which, together with free reduction, can be used to reduce any word over the standard generators of G to a geodesic word in G in quadratic time. This result builds on work of Holt and Rees, and of Blasco, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively.
Conjugacy in Artin groups and applications to the classification of surfaces
Artin groups of type (2,3,n)
Recognizing geometric 3-manifold groups using the word problem
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