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A Norm on the Fundamental Group of Non-Haken 3-Manifolds

Kerry N. Jones
Proceedings of the American Mathematical Society
Vol. 120, No. 1 (Jan., 1994), pp. 305-309
DOI: 10.2307/2160200
Stable URL: http://www.jstor.org/stable/2160200
Page Count: 5
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A Norm on the Fundamental Group of Non-Haken 3-Manifolds
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Abstract

A canonical (presentation-independent) conjugacy-invariant norm is constructed on the fundamental group of any 3-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.

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