TY - JOUR
T1 - Milnor invariants of covering links
AU - Kobayashi, Natsuka
AU - Wada, Kodai
AU - Yasuhara, Akira
N1 - Funding Information:
The authors would like to express their gratitude to the referee for his/her thoughtful reading of the manuscript and helpful comments. The third author was partially supported by a JSPS Grant-in-Aid for Scientific Research (C) (#26400081).
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/6/15
Y1 - 2017/6/15
N2 - 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.
AB - 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.
KW - Clasper
KW - Cobordism
KW - Covering linkage invariant
KW - Link-homotopy
KW - Milnor invariant
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U2 - 10.1016/j.topol.2017.04.002
DO - 10.1016/j.topol.2017.04.002
M3 - Article
AN - SCOPUS:85026286942
SN - 0166-8641
VL - 224
SP - 60
EP - 72
JO - Topology and its Applications
JF - Topology and its Applications
ER -