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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Milnor’s invariants and self $C_{k}$-equivalence
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by Thomas Fleming and Akira Yasuhara PDF
Proc. Amer. Math. Soc. 137 (2009), 761-770 Request permission

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
  • Email: tfleming@math.ucsd.edu
  • Akira Yasuhara
  • Affiliation: Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo 184-8501, Japan
  • MR Author ID: 320076
  • Email: yasuhara@u-gakugei.ac.jp
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 761-770
  • MSC (2000): Primary 57M25
  • DOI: https://doi.org/10.1090/S0002-9939-08-09521-X
  • MathSciNet review: 2448599