Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 57M25, 57M05

Retrieve articles in all journals with MSC (2010): 57M25, 57M05

Additional Information

Zhiqing Yang
Affiliation: School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, People’s Republic of China

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.

American Mathematical Society