WIDTHS OF SUBGROUPS

Rita Gitik Mahan Mitra Eliyahu Rips Michah Sageev

Abstract. Let H be a subgroup of a group G. We say that the conjugates

{g_{i}^{−1}Hg_{i} | 1 ≤ i ≤ n}

of H are essentially distinct if Hg_{i} ≠ Hg_{j} for i ≠ j. 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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