Embeddings of locally compact hyperbolic groups into L-p-spaces

作者：Cave Chris^*; Dreesen Dennis

来源：Topology and Its Applications, 2016, 214: 66-88.

DOI：10.1016/j.topol.2016.09.009

• Hyperbolic groups
• Groups acting on Banach space

In the last years, there has been a large amount of research on embeddability properties of finitely generated hyperbolic groups. In this paper, we elaborate on the more general class of locally compact hyperbolic groups. We compute the equivariant L-p-compression in a number of locally compact examples, such as the groups SO(n,1). Next, we show that although there are locally compact, non discrete hyperbolic groups G with Kazhdan's property (T), it is true that any locally compact hyperbolic group admits a proper affine isometric action on an L-p-space for p larger than the Ahlfors regular conformal dimension of partial derivative G. This answers a question asked by Yves de Cornulier. Finally, we elaborate on the locally compact version of property A and show that, as in the discrete case, a locally compact second countable group has property A if its non-equivariant compression is greater than 1/2.

• 出版日期2016-12-1