A norm on the fundamental group of non-Haken -manifolds
Author: Kerry N. Jones
Journal: Proc. Amer. Math. Soc. 120 (1994), 305-309
MSC: Primary 57M05; Secondary 20F38, 57N10
MathSciNet review: 1186989
Abstract: A canonical (presentation-independent) conjugacy-invariant norm is constructed on the fundamental group of any -manifold which is orientable, irreducible, has infinite fundamental group, and contains no incompressible surface. More generally, this norm exists on any torsion-free group whose commutator quotient is finite. This norm is then computed explicitly in an example which shows that the induced metric on the group is not quasi-isometric to any word metric.
Keywords: Non-Haken -manifold, fundamental group, geometric group theory
Article copyright: © Copyright 1994 American Mathematical Society