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
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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.

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Additional Information

Thomas Fleming
Affiliation: Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112

Akira Yasuhara
Affiliation: Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo 184-8501, Japan

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.