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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A norm on the fundamental group of non-Haken $ 3$-manifolds


Author: Kerry N. Jones
Journal: Proc. Amer. Math. Soc. 120 (1994), 305-309
MSC: Primary 57M05; Secondary 20F38, 57N10
MathSciNet review: 1186989
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1186989-1
PII: S 0002-9939(1994)1186989-1
Keywords: Non-Haken $ 3$-manifold, fundamental group, geometric group theory
Article copyright: © Copyright 1994 American Mathematical Society