Infinitely presented small cancellation groups have the Haagerup property

Abstract

We prove the Haagerup property (= Gromov's a-T-menability) for finitely generated groups defined by infinite presentations satisfying the C'(1/6)-small cancellation condition. We deduce that these groups are coarsely embeddable into a Hilbert space and that the strong Baum-Connes conjecture holds for them. The result is a first non-trivial advancement in understanding groups with such properties among infinitely presented non-amenable direct limits of hyperbolic groups. The proof uses the structure of a space with walls introduced by Wise. As the main step we show that C'(1/6)-complexes satisfy the linear separation property.

16 pages, minor modifications to v3

References in corpus (2)

• Isometric group actions on Banach spaces and representations vanishing at infinity
• Geometry of infinitely presented small cancellation groups, Rapid Decay and quasi-homomorphisms

Cited by in corpus (1)

• Graphical small cancellation groups with the Haagerup property