Topology Atlas | Conferences

Knots in Washington XLI
December 4-6, 2015
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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The Milnor invariants of clover links
by
Kodai Wada
Waseda University
Coauthors: Akira Yasuhara

J.P. Levine introduced a clover link to investigate the indeterminacy of the Milnor invariants of a link. It is shown that for a clover link, the Milnor numbers of length at most 2k+1 are well-defined if those of length at most k vanish, and that the Milnor numbers of length at least 2k+2 are not well-defined if those of length k+1 survive. For a clover link c with the Milnor numbers of length at most k vanishing, we show that the Milnor number μc(I) for a sequence I is well-defined up to the greatest common devisor of μc(J)'s, where J is a subsequence of I obtained by removing at least k+1 indices. Moreover, if I is a non-repeated sequence with length 2k+2, the possible range of μc(I) is given explicitly. As an application, we give an edge-homotopy classification of 4-clover links.

Date received: October 7, 2015

Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-09.