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Distance between toroidal surgeries on hyperbolic knots in the  -sphere
Author(s):
Masakazu
Teragaito
Journal:
Trans. Amer. Math. Soc.
358
(2006),
1051-1075.
MSC (2000):
Primary 57M25
Posted:
April 13, 2005
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Abstract:
For a hyperbolic knot in the  -sphere, at most finitely many Dehn surgeries yield non-hyperbolic  -manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed  -manifold containing an incompressible torus. The slope corresponding to a toroidal surgery, called a toroidal slope, is known to be integral or half-integral. We show that the distance between two integral toroidal slopes for a hyperbolic knot, except the figure-eight knot, is at most four.
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Additional Information:
Masakazu
Teragaito
Affiliation:
Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
Email:
teragai@hiroshima-u.ac.jp
DOI:
10.1090/S0002-9947-05-03703-7
PII:
S 0002-9947(05)03703-7
Keywords:
Dehn surgery,
toroidal surgery,
knot
Received by editor(s):
December 10, 2003
Received by editor(s) in revised form:
April 7, 2004
Posted:
April 13, 2005
Additional Notes:
This work was partially supported by the Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), 14540082.
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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