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Widths of Subgroups |
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| Authors: | Rita Gitik Mahan Mitra Eliyahu Rips Michah Sageev |
| Institution: | Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 ; Department of Mathematics, University of California, Berkeley, California 94720 ; Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel ; Department of Mathematics, University of Southampton, Southampton, England |
| Abstract: | We say that the width of an infinite subgroup  in  is  if there exists a collection of  essentially distinct conjugates of  such that the intersection of any two elements of the collection is infinite and  is maximal possible. We define the width of a finite subgroup to be  . We prove that a quasiconvex subgroup of a negatively curved group has finite width. It follows that geometrically finite surfaces in closed hyperbolic  -manifolds satisfy the  -plane property for some  . |
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