Non-integral toroidal surgery

on hyperbolic knots in

Authors:
C. Mc A. Gordon, Y-Q. Wu and X. Zhang

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1869-1879

MSC (1991):
Primary 57N10, 57M25

Published electronically:
November 24, 1999

MathSciNet review:
1644022

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a hyperbolic knot in admits at most one non-integral Dehn surgery producing a toroidal manifold.

**[CGLS]**Marc Culler, C. McA. Gordon, J. Luecke, and Peter B. Shalen,*Dehn surgery on knots*, Ann. of Math. (2)**125**(1987), no. 2, 237–300. MR**881270**, 10.2307/1971311**[EM]**Mario Eudave-Muñoz,*Non-hyperbolic manifolds obtained by Dehn surgery on hyperbolic knots*, Geometric topology (Athens, GA, 1993) AMS/IP Stud. Adv. Math., vol. 2, Amer. Math. Soc., Providence, RI, 1997, pp. 35–61. MR**1470720****[Go1]**C. McA. Gordon,*Dehn filling: a survey*, Knot theory (Warsaw, 1995) Banach Center Publ., vol. 42, Polish Acad. Sci. Inst. Math., Warsaw, 1998, pp. 129–144. MR**1634453****[Go2]**C. McA. Gordon,*Boundary slopes of punctured tori in 3-manifolds*, Trans. Amer. Math. Soc.**350**(1998), no. 5, 1713–1790. MR**1390037**, 10.1090/S0002-9947-98-01763-2**[GL1]**C. McA. Gordon and J. Luecke,*Dehn surgeries on knots creating essential tori. I*, Comm. Anal. Geom.**3**(1995), no. 3-4, 597–644. MR**1371211**, 10.4310/CAG.1995.v3.n4.a3**[GL2]**-,*Dehn surgeries on knots creating essential tori, II*, Comm. in Analy. and Geo. (to appear).**[K]**R. Kirby,*Problems in low-dimensional topology*, Proceedings of Georgia Topology Conference, Part 2, 1996, pp. 35-473. CMP**98:01****[Th]**W. Thurston,*The Geometry and Topology of 3-manifolds*, Princeton University, 1978.**[W]**Christof Mackrodt,*Representation forms for metacyclic groups*, Manuscripta Math.**73**(1991), no. 3, 261–287. MR**1132140**, 10.1007/BF02567641

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Additional Information

**C. Mc A. Gordon**

Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

Email:
gordon@math.utexas.edu

**Y-Q. Wu**

Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Email:
wu@math.uiowa.edu

**X. Zhang**

Affiliation:
Department of Mathematics, State University of New York–Buffalo, Buffalo, New York 14214

Email:
xinzhang@math.buffalo.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05201-6

Received by editor(s):
May 20, 1997

Received by editor(s) in revised form:
August 3, 1998

Published electronically:
November 24, 1999

Additional Notes:
The first author was partially supported by NSF grant DMS 9626550.

The first and second authors were supported in part by Research at MSRI NSF grant #DMS 9022140.

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 2000
American Mathematical Society