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ARTIN GROUPS OF INFINITE TYPE: TRIVIAL CENTERS AND ACYLINDRICAL HYPERBOLICITY
Journal article   Peer reviewed

ARTIN GROUPS OF INFINITE TYPE: TRIVIAL CENTERS AND ACYLINDRICAL HYPERBOLICITY

Ruth Charney and Rose Morris-Wright
Proceedings of the American Mathematical Society, Vol.147(9), pp.3675-3689
09/01/2019

Abstract

Mathematics, Applied Science & Technology Mathematics Physical Sciences
While finite type Artin groups and right-angled Artin groups are well understood, little is known about more general Artin groups. In this paper we use the action of an infinite type Artin group A(Gamma) on a CAT(0) cube complex to prove that A(Gamma) has trivial center providing Gamma is not the star of a single vertex, and is acylindrically hyperbolic providing Gamma is not a join.

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