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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an exact sequence of hyperbolic groups induced by an automorphism of the free group . Let be a finitely generated distorted subgroup of . Then there exist and a free factor of such that the conjugacy class of is preserved by 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.

**1.**M. Bestvina and M. Feighn,*A combination theorem for negatively curved groups*, J. Differential Geom.**35**(1992), no. 1, 85–101. MR**1152226****2.**M. Bestvina, M. Feighn, and M. Handel. The Tits' alternative for Out() I: Dynamics of exponentially growing automorphisms.*preprint*.**3.**M. Bestvina, M. Feighn, and M. Handel,*Laminations, trees, and irreducible automorphisms of free groups*, Geom. Funct. Anal.**7**(1997), no. 2, 215–244. MR**1445386**, 10.1007/PL00001618**4.**Mladen Bestvina and Michael Handel,*Train tracks and automorphisms of free groups*, Ann. of Math. (2)**135**(1992), no. 1, 1–51. MR**1147956**, 10.2307/2946562**5.**J. Cannon and W. P. Thurston. Group Invariant Peano Curves.*preprint*.**6.**Benson Farb,*The extrinsic geometry of subgroups and the generalized word problem*, Proc. London Math. Soc. (3)**68**(1994), no. 3, 577–593. MR**1262309**, 10.1112/plms/s3-68.3.577**7.**M. Gromov,*Asymptotic invariants of infinite groups*, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295. MR**1253544****8.**M. Gromov,*Hyperbolic groups*, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR**919829**, 10.1007/978-1-4613-9586-7_3**9.**M. Mitra. Ending Laminations for Hyperbolic Group Extensions.*Geom. Funct. Anal. vol.7 No. 2*, pages 379-402, 1997. CMP**(97:11****10.**M. Mitra. PhD Thesis, U.C.Berkeley. 1997.**11.**M. Mitra. Cannon-Thurston Maps for Hyperbolic Group Extensions.*Topology*, 1998.**12.**Peter Scott,*Subgroups of surface groups are almost geometric*, J. London Math. Soc. (2)**17**(1978), no. 3, 555–565. MR**0494062**

Peter Scott,*Correction to: “Subgroups of surface groups are almost geometric” [J. London Math. Soc. (2) 17 (1978), no. 3, 555–565; MR0494062 (58 #12996)]*, J. London Math. Soc. (2)**32**(1985), no. 2, 217–220. MR**811778**, 10.1112/jlms/s2-32.2.217**13.**G. P. Scott and G. A. Swarup,*Geometric finiteness of certain Kleinian groups*, Proc. Amer. Math. Soc.**109**(1990), no. 3, 765–768. MR**1013981**, 10.1090/S0002-9939-1990-1013981-6**14.**Hamish Short,*Quasiconvexity and a theorem of Howson’s*, Group theory from a geometrical viewpoint (Trieste, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 168–176. MR**1170365**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
20F32,
57M50

Retrieve articles in all journals with MSC (1991): 20F32, 57M50

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

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