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2011 Complexes and exactness of certain Artin groups
Erik Guentner, Graham A Niblo
Algebr. Geom. Topol. 11(3): 1471-1495 (2011). DOI: 10.2140/agt.2011.11.1471

Abstract

In his work on the Novikov conjecture, Yu introduced Property A as a readily verified criterion implying coarse embeddability. Studied subsequently as a property in its own right, Property A for a discrete group is known to be equivalent to exactness of the reduced group C–algebra and to the amenability of the action of the group on its Stone–Čech compactification. In this paper we study exactness for groups acting on a finite dimensional CAT(0) cube complex. We apply our methods to show that Artin groups of type FC are exact. While many discrete groups are known to be exact the question of whether every Artin group is exact remains open.

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Erik Guentner. Graham A Niblo. "Complexes and exactness of certain Artin groups." Algebr. Geom. Topol. 11 (3) 1471 - 1495, 2011. https://doi.org/10.2140/agt.2011.11.1471

Information

Received: 23 August 2010; Revised: 4 January 2011; Accepted: 24 January 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1245.20040
MathSciNet: MR2821432
Digital Object Identifier: 10.2140/agt.2011.11.1471

Subjects:
Primary: 20F36, 20F65, 43A99
Secondary: 51F15

Rights: Copyright © 2011 Mathematical Sciences Publishers

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