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

 

Infinite sequences of mutually non-conjugate surface braids representing same surface-links


Author: Masahide Iwakiri
Journal: Proc. Amer. Math. Soc. 140 (2012), 357-366
MSC (2010): Primary 57Q45
Published electronically: May 25, 2011
MathSciNet review: 2833546
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Abstract: We give an infinite sequence of mutually non-conjugate surface braids with same degree representing the trivial surface-link with at least two components and a pair of non-conjugate surface braids with same degree representing a spun $ (2,t)$-torus knot for $ t\geq 3$. To give these examples, we introduce new invariants of conjugacy classes of surface braids via colorings by Alexander quandles or core quandles of groups.


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Additional Information

Masahide Iwakiri
Affiliation: Graduate School of Science, Osaka City University, 3-3-138 Sugimoto Sumiyoshi-ku, Osaka 558-8585, Japan
Address at time of publication: Graduate School of Science and Engineering, Saga University, 1 Honjo-machi, Saga City, Saga, 840-8502, Japan
Email: iwakiri@sci.osaka-cu.ac.jp, iwakiri@ms.saga-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10893-1
PII: S 0002-9939(2011)10893-1
Received by editor(s): July 16, 2010
Received by editor(s) in revised form: November 11, 2010, and November 12, 2010
Published electronically: May 25, 2011
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.