Incommensurability criteria for Kleinian groups
Author:
James W. Anderson
Journal:
Proc. Amer. Math. Soc. 130 (2002), 253258
MSC (1991):
Primary 57M50, 30F40; Secondary 20H10
Published electronically:
April 26, 2001
MathSciNet review:
1855643
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Abstract: The purpose of this note is to present a criterion for an infinite collection of distinct hyperbolic 3manifolds to be commensurably infinite. (Here, a collection of hyperbolic 3manifolds is commensurably infinite if it contains representatives from infinitely many commensurability classes.) Namely, such a collection is commensurably infinite if there is a uniform upper bound on the volumes of the manifolds in . There is a related criterion for an infinite collection of distinct finitely generated Kleinian groups with nonempty domain of discontinuity to be commensurably infinite. (Here, a collection of Kleinian groups is commensurably infinite if it is infinite modulo the combined equivalence relations of commensurability and conjugacy in .) Namely, such a collection is commensurably infinite if there is a uniform bound on the areas of the quotient surfaces of the groups in .
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Additional Information
James W. Anderson
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, England
Email:
j.w.anderson@maths.soton.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002993901060762
PII:
S 00029939(01)060762
Keywords:
Kleinian group,
hyperbolic 3manifold,
commensurable
Received by editor(s):
May 18, 2000
Published electronically:
April 26, 2001
Communicated by:
Jozef Dodziuk
Article copyright:
© Copyright 2001
American Mathematical Society
