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

DOI:
https://doi.org/10.1090/S0002-9947-98-01792-9

MathSciNet review:
1389776

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Abstract | References | Similar Articles | Additional Information

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

MR Author ID:
366122

Email:
mes@maths.soton.ac.uk

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