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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a theorem of Scott and Swarup


Author: Mahan Mitra
Journal: Proc. Amer. Math. Soc. 127 (1999), 1625-1631
MSC (1991): Primary 20F32, 57M50
Published electronically: February 17, 1999
MathSciNet review: 1610757
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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 $H$. Let $H_1 ( \subset H)$ be a finitely generated distorted subgroup of $G$. Then there exist $N > 0$ and a free factor $K$ of $H$ such that the conjugacy class of $K$ is preserved by $\phi^N$ and $H_1$ contains a finite index subgroup of a conjugate of $K$. This is an analog of a theorem of Scott and Swarup for surfaces in hyperbolic 3-manifolds.


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Additional Information

Mahan Mitra
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720
Address at time of publication: Institute of Mathematical Sciences, C.I.T. Campus, Madras (Chennai) - 600113, India
Email: mitra@imsc.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04935-7
PII: S 0002-9939(99)04935-7
Received by editor(s): September 22, 1997
Published electronically: February 17, 1999
Additional Notes: The author’s research was partly supported by an Alfred P. Sloan Doctoral Dissertation Fellowship, Grant No. DD 595
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society