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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On embedding the infinite cyclic coverings of knot complements into three sphere


Author: Zhiqing Yang
Journal: Proc. Amer. Math. Soc. 138 (2010), 1153-1157
MSC (2010): Primary 57M25; Secondary 57M05
Published electronically: October 28, 2009
MathSciNet review: 2566580
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Abstract: We construct a class of knots with the CI$ {}^*$ property, that is, $ \pi_1(M(n)\mid \partial M(n))\neq \{e\}$ for some $ n>0$. It follows that the infinite cyclic covering of such a knot cannot be embedded in any compact 3-manifold.


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Additional Information

Zhiqing Yang
Affiliation: School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, People’s Republic of China
Email: yangzhq@dlut.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10137-5
PII: S 0002-9939(09)10137-5
Keywords: infinite cyclic covering, knot, Seifert surface, knot group
Received by editor(s): July 26, 2008
Received by editor(s) in revised form: February 26, 2009, July 17, 2009, and July 29, 2009
Published electronically: October 28, 2009
Additional Notes: The author is supported by a grant (No. 100771023) of NSFC and a grant from Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (20070141035).
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.