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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Seifert-fibered surgeries which do not arise from primitive/Seifert-fibered constructions


Authors: Thomas Mattman, Katura Miyazaki and Kimihiko Motegi
Journal: Trans. Amer. Math. Soc. 358 (2006), 4045-4055
MSC (2000): Primary 57M25
Published electronically: September 22, 2005
MathSciNet review: 2219009
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Abstract: We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert-fibered surgeries arise from Dean's primitive/Seifert-fibered construction. The $(-3,3,5)$-pretzel knot belongs to both of the infinite families.


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Additional Information

Thomas Mattman
Affiliation: Department of Mathematics and Statistics, California State University–Chico, Chico, California 95929-0525
Email: TMattman@CSUChico.edu

Katura Miyazaki
Affiliation: Faculty of Engineering, Tokyo Denki University, Tokyo 101-8457, Japan
Email: miyazaki@cck.dendai.ac.jp

Kimihiko Motegi
Affiliation: Department of Mathematics, Nihon University, Tokyo 156-8550, Japan
Email: motegi@math.chs.nihon-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03798-0
PII: S 0002-9947(05)03798-0
Keywords: Dehn surgery, hyperbolic knot, Seifert fiber space, primitive/Seifert-fibered construction
Received by editor(s): January 20, 2003
Received by editor(s) in revised form: June 28, 2004
Published electronically: September 22, 2005
Additional Notes: The first author was supported in part by grants from NSERC and FCAR
The second author was supported in part by Grant-in-Aid for Scientific Research (No.\ 40219978), The Ministry of Education, Culture, Sports, Science and Technology, Japan.
Dedicated: Dedicated to Cameron McA. Gordon on the occasion of his 60th birthday
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.