# Generalizations of Agol's inequality and nonexistence of tight laminations

Research paper by Thilo Kuessner

Indexed on: 28 Apr '11Published on: 28 Apr '11Published in: Mathematics - Geometric Topology

#### 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.