A conjecture about Artin–Tits groups
Copyright policy )A conjecture about Artin–Tits groups
We conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial factors ss^{-1} or s^{-1}s. Here we make this statement precise and explain how it can be seen as a weak form of hyperbolicity. We prove the conjecture in the case of Artin-Tits groups of type FC, and we discuss various possible approaches for further extensions, in particular a syntactic argument that works at least in the right-angled case.
word problem, Generators, relations, and presentations of groups, hyperbolicity, Free semigroups, generators and relations, word problems, Artin-Tits presentations, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), monoids, Group Theory (math.GR), Braid groups; Artin groups, Hyperbolic groups and nonpositively curved groups, FOS: Mathematics, Artin-Tits groups, Mathematics - Group Theory
word problem, Generators, relations, and presentations of groups, hyperbolicity, Free semigroups, generators and relations, word problems, Artin-Tits presentations, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), monoids, Group Theory (math.GR), Braid groups; Artin groups, Hyperbolic groups and nonpositively curved groups, FOS: Mathematics, Artin-Tits groups, Mathematics - Group Theory
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