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Non-integral toroidal surgery on hyperbolic knots in 
Author(s):
C.
Mc A.
Gordon;
Y-Q.
Wu;
X.
Zhang
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1869-1879.
MSC (1991):
Primary 57N10, 57M25
Posted:
November 24, 1999
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Abstract:
It is shown that a hyperbolic knot in  admits at most one non-integral Dehn surgery producing a toroidal manifold.
References:
- [CGLS]
- M. Culler, C. Gordon, J. Luecke and P. Shalen, Dehn surgery on knots, Annals Math. 125 (1987), 237-300. MR 88a:57026
- [EM]
- M. Eudave-Munoz, Non-hyperbolic manifolds obtained by Dehn surgery on hyperbolic knots, Proceedings of Georgia Topology Conference 1996, Part 1, pp. 35-61. MR 98i:57007
- [Go1]
- C. Gordon, Dehn filling: a survey, Knot Theory, Banach Center Publications Vol. 42, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 1998. MR 99e:57028
- [Go2]
- -, Boundary slopes of punctured tori in 3-manifolds, Trans. Amer. Math. Soc. 350 (1998), 1713-1790. MR 98h:57032
- [GL1]
- C. Gordon and J. Luecke, Dehn surgeries on knots creating essential tori, I, Comm. in Analy. and Geo. 3 (1995), 597-644. MR 96k:57003
- [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]
- Y-Q. Wu, The reducibility of surgered 3-manifolds, Topology Appl. 43 (1992), 213-218. MR 93c:57032
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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:
10.1090/S0002-9939-99-05201-6
PII:
S 0002-9939(99)05201-6
Received by editor(s):
May 20, 1997
Received by editor(s) in revised form:
August 3, 1998
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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