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Article Dans Une Revue Algebraic and Geometric Topology Année : 2021

Parabolic subgroups acting on the additional length graph

Résumé

Let A not equal A(1), A(2), I-2m be an irreducible Artin-Tits group of spherical type. We show that the periodic elements of A and the elements preserving some parabolic subgroup of A act elliptically on the additional length graph C-AL (A), a hyperbolic, infinite diameter graph associated to A constructed by Calvez and Wiest to show that A/Z(A) is acylindrically hyperbolic. We use these results to find an element g is an element of 2 A such that < P, g > congruent to P * < g > for every proper standard parabolic subgroup P of A. The length of g is uniformly bounded with respect to the Garside generators, independently of A. This allows us to show that, in contrast with the Artin generators case, the sequence {omega(A(n), S)}(n is an element of N) of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity.

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Dates et versions

hal-03466994 , version 1 (06-12-2021)

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Citer

Yago Antolín, María Cumplido. Parabolic subgroups acting on the additional length graph. Algebraic and Geometric Topology, 2021, 21 (4), pp.1791-1816. ⟨10.2140/agt.2021.21.1791⟩. ⟨hal-03466994⟩
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