Warped cones and Haagerup property

TL;DR

This paper explores the relationship between warped cones and group properties, showing how embeddability relates to the Haagerup property and how Kazhdan's property (T) influences geometric properties of warped cones.

Contribution

It establishes new links between warped cone geometry and group properties like the Haagerup property and property (T).

Findings

Fibred coarse embeddability of warped cones implies the Haagerup property.

Kazhdan's property (T) of a group implies geometric property (T) of the warped cone.

Provides new insights into the geometric group theory of warped cones.

Abstract

In this paper we show that the fibred coarse embeddability of a warped cone implies the Haagerup property of the appropriate group. Moreover, Kazhdan's property (T) of the group implies geometric property (T) of the warped cone.