An isoperimetric inequality for Artin groups of finite type. (English) Zbl 0798.20030

Tatsuoka, Kay

Trans. Am. Math. Soc. 339, No. 2, 537-551 (1993).

W. Thurston has shown that the braid groups are automatic [preprint] and R. Charney has generalised this result to Artin groups of finite type [Math. Ann. 292, No. 4, 671-684 (1992; Zbl 0736.57001)]. It is known that all automatic groups satisfy a quadratic isoperimetric inequality and the author directly verifies that Artin groups of finite type satisfy the above-mentioned inequality. The next result appears to be new: the word problem in Artin groups of finite type is solvable in quadratic time.

Reviewer: G.A.Noskov (Omsk)

MSC:

20F36	Braid groups; Artin groups
20F10	Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
57M05	Fundamental group, presentations, free differential calculus

Keywords:

braid groups; automatic groups; quadratic isoperimetric inequality; Artin groups of finite type; word problem; quadratic time

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