Widths of Subgroups

Gitik, Rita; Mitra, Mahan; Rips, Eliyahu; Sageev, Michah

doi:10.1090/S0002-9947-98-01792-9

Widths of Subgroups
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by Rita Gitik, Mahan Mitra, Eliyahu Rips and Michah Sageev

Trans. Amer. Math. Soc. 350 (1998), 321-329

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

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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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