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Transactions of the American Mathematical Society

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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

Mahan Mitra
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

Eliyahu Rips
Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel

Michah Sageev
Affiliation: Department of Mathematics, University of Southampton, Southampton, England

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

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