Generalizations of Agol’s inequality and nonexistence of tight laminations

Thilo Kuessner

Vol. 251 (2011), No. 1, 109–172

DOI: 10.2140/pjm.2011.251.109

Abstract

We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions.

In the special case of 3-manifolds, this yields a generalization of Agol’s inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the existence of tight laminations with nonempty guts on 3-manifolds of small simplicial volume.

Keywords

lamination, hyperbolic, 3-manifold, volume, Gromov norm, tight, Weeks manifold, simplicial, simplex, straightening

Mathematical Subject Classification 2000

Primary: 57R30

Secondary: 53C23, 57M27, 57N10, 57M50

Milestones

Received: 15 June 2008

Accepted: 25 January 2010

Published: 22 April 2011