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
DOI:
https://doi.org/10.1090/S0002-9939-1994-1186989-1
MathSciNet review:
1186989
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Abstract | References | Similar Articles | Additional Information
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.
- [He] John Hempel, 3-Manifolds, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. Ann. of Math. Studies, No. 86. MR 0415619
-manifolds, Princeton Univ. Press, Princeton, NJ, 1976. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57M05, 20F38, 57N10
Retrieve articles in all journals with MSC: 57M05, 20F38, 57N10
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1994-1186989-1
Keywords:
Non-Haken 
-manifold,
fundamental group,
geometric group theory
Article copyright:
© Copyright 1994
American Mathematical Society
