Rank gradient of small covers

Darlan Girão

Vol. 266 (2013), No. 1, 23–29

DOI: 10.2140/pjm.2013.266.23

Abstract

We prove that if M→P is a small cover of a compact right-angled hyperbolic polyhedron then M admits a cofinal tower of finite sheeted covers with positive rank gradient. As a corollary, if π₁(M) is commensurable with the reflection group of P, then M admits a cofinal tower of finite sheeted covers with positive rank gradient.

Keywords

rank gradient, hyperbolic 3-manifolds

Mathematical Subject Classification 2010

Primary: 57M05

Milestones

Received: 3 September 2012

Revised: 2 January 2013

Accepted: 16 January 2013

Published: 23 September 2013