Complexes and exactness of certain Artin groups

Guentner, Erik¹ ; Niblo, Graham A²

¹Department of Mathematics, University of Hawai’i at Manoa, 2565 McCarthy Mall, Honolulu HI 96822, USA
²School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK

Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1471-1495

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.1471

Keywords: Property $A$, exactness, Artin group, $\mathrm{CAT}(0)$ cube complex

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