Widths of Subgroups

Authors:
  • RGRita Gitik
    Rita Gitik
  • MMMahan Mitra
    Mahan Mitra
  • EREliyahu Rips
    Eliyahu Rips
  • MSMichah Sageev
    Michah Sageev
Open Access
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Abstract
We say that the width of an infinite subgroup H H in G G is n n if there exists a collection of n n essentially distinct conjugates of H H such that the intersection of any two elements of the collection is infinite and n n is maximal possible. We define the width of a finite subgroup to be 0 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 3 -manifolds satisfy the k k -plane property for some k k .