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On a theorem of Scott and Swarup

Authors:	Mahan Mitra

Institution:	Department of Mathematics, University of California at Berkeley, Berkeley, California 94720

Abstract:	Let $1 \rightarrow H \rightarrow G \rightarrow \mathbb{Z} \rightarrow 1$ be an exact sequence of hyperbolic groups induced by an automorphism $\phi$ of the free group . Let $H_1 ( \subset H)$ be a finitely generated distorted subgroup of . Then there exist and a free factor of such that the conjugacy class of is preserved by $\phi^N$ and contains a finite index subgroup of a conjugate of . This is an analog of a theorem of Scott and Swarup for surfaces in hyperbolic 3-manifolds.

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