arXiv subjects
Publications and source records attributed to Rubén Blasco-García.
We give a quadratic-time explicit and computable algorithm to solve the word problem for Artin groups that do not contain any relations of length 3. Furthermore, we prove that, given two geodesic words representing the same element, one can obtain one from the other by using a set of homogeneous relations that never increase the word length.
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-García, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively.
We explicitly compute the homology groups with coefficients in a field of characteristic zero of cocyclic subgroups or even Artin groups of FC-type. We also give some partial results in the case when the coefficients are taken in a field of prime characteristic.