Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Milnor's invariants and self $ C_{k}$-equivalence


Authors: Thomas Fleming and Akira Yasuhara
Journal: Proc. Amer. Math. Soc. 137 (2009), 761-770
MSC (2000): Primary 57M25
Published electronically: August 28, 2008
MathSciNet review: 2448599
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It has long been known that a Milnor invariant with no repeated index is an invariant of link homotopy. We show that Milnor's invariants with repeated indices are invariants not only of isotopy, but also of self $ C_{k}$-equivalence. Here self $ C_{k}$-equivalence is a natural generalization of link homotopy based on certain degree $ k$ clasper surgeries, which provides a filtration of link homotopy classes.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M25

Retrieve articles in all journals with MSC (2000): 57M25


Additional Information

Thomas Fleming
Affiliation: Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
Email: tfleming@math.ucsd.edu

Akira Yasuhara
Affiliation: Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo 184-8501, Japan
Email: yasuhara@u-gakugei.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09521-X
PII: S 0002-9939(08)09521-X
Received by editor(s): December 4, 2006
Received by editor(s) in revised form: February 4, 2008
Published electronically: August 28, 2008
Additional Notes: The first author was supported by a Post-Doctoral Fellowship for Foreign Researchers ($#$PE05003) from the Japan Society for the Promotion of Science.
The second author is partially supported by a Grant-in-Aid for Scientific Research (C) ($#$18540071) of the Japan Society for the Promotion of Science.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.