Discrete fundamental groups of Warped Cones and expanders

Abstract

In this paper we compute the discrete fundamental groups of warped cones. As an immediate consequence, this allows us to show that there exist coarsely simply-connected expanders and superexpanders. This also provides a strong coarse invariant of warped cones and implies that many warped cones cannot be coarsely equivalent to any box space.

arXiv comment39 pages, 5 figures. A few minor improvements since the last version. To appear in Mathematische Annalen