A non-Haken hyperbolic 3-manifold covered by a surface bundle

Alan W. Reid

Vol. 167 (1995), No. 1, 163–182

DOI: 10.2140/pjm.1995.167.163

Abstract

The question as to whether a finite volume hyperbolic 3-manifold has a finite cover which fibers over the circle, seems, at present, completely mysterious. In this paper we give the first explicit examples of non-Haken hyperbolic 3-manifolds covered by a manifold that fibers of the circle. The methods used are arithmetic using the theory of quaternion algebras.

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 57N10

Milestones

Received: 18 August 1992

Revised: 8 September 1992

Published: 1 January 1995