Milnor invariants of covering links

Natsuka Kobayashi,Kodai Wada,Akira Yasuhara

doi:10.1016/j.topol.2017.04.002

Natsuka Kobayashi, Kodai Wada + Show 1 more

Open Access

https://doi.org/10.1016/j.topol.2017.04.002

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Journal: Topology and its Applications	Publication Date: May 8, 2017
License type: elsevier-specific: oa user license

Affiliation: Waseda University, Tsuda University

Abstract

We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants of covering links is a cobordism invariant of a link, and this invariant can detect some links undetected by the ordinary Milnor invariants. Moreover, for a Brunnian link L, the first non-vanishing Milnor invariant of L is modulo-2 congruent to a sum of Milnor invariants of covering links. As a consequence, a sum of linking numbers of ‘iterated’ covering links gives the first non-vanishing Milnor invariant of L modulo 2.

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