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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Widths of Subgroups


Authors: Rita Gitik, Mahan Mitra, Eliyahu Rips and Michah Sageev
Journal: Trans. Amer. Math. Soc. 350 (1998), 321-329
MSC (1991): Primary 20F32, 57M07
MathSciNet review: 1389776
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Abstract: We say that the width of an infinite subgroup $H$ in $G$ is $n$ if there exists a collection of $n$ essentially distinct conjugates of $H$ such that the intersection of any two elements of the collection is infinite and $n$ is maximal possible. We define the width of a finite subgroup to be $0$. We prove that a quasiconvex subgroup of a negatively curved group has finite width. It follows that geometrically finite surfaces in closed hyperbolic $3$-manifolds satisfy the $k$-plane property for some $k$.


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Additional Information

Rita Gitik
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: ritagtk@math.lsa.umich.edu

Mahan Mitra
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: mitra@math.berkeley.edu

Eliyahu Rips
Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel
Email: rips@sunset.huji.ac.il

Michah Sageev
Affiliation: Department of Mathematics, University of Southampton, Southampton, England
Email: mes@maths.soton.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01792-9
PII: S 0002-9947(98)01792-9
Received by editor(s): September 19, 1995
Received by editor(s) in revised form: March 25, 1996
Additional Notes: Research of the first author supported in part by NSF grant DMS 9022140.
Article copyright: © Copyright 1998 American Mathematical Society