Abstract
This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the center, the word problem, and the cohomology (K(π, 1) problem). It is also an opportunity to prove three new results concerning these questions: (1) if all free of infinity Artin-Tits groups are torsion free, then all Artin-Tits groups will be torsion free; (2) If all free of infinity irreducible non-spherical type Artin-Tits groups have a trivial center then all irreducible non-spherical type Artin-Tits groups will have a trivial center; (3) if all free of infinity Artin-Tits groups have solutions to the word problem, then all Artin-Tits groups will have solutions to the word problem. Recall that an Artin-Tits group is free of infinity if its Coxeter graph has no edge labeled by ∞.
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Godelle, E., Paris, L. (2012). Basic questions on Artin-Tits groups. In: Bjorner, A., Cohen, F., De Concini, C., Procesi, C., Salvetti, M. (eds) Configuration Spaces. CRM Series. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-431-1_13
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DOI: https://doi.org/10.1007/978-88-7642-431-1_13
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