Geodesic
Links with trivial Alexander module and nontrivial Milnor invariants
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 17 (2015), pp. 41-49

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Cochran constructed many links with Alexander module that of the unlink and some nonvanishing Milnor invariants, using as input commutators in a free group and as an invariant the longitudes of the links. We present a different and conjecturally complete construction, that uses elementary properties of clasper surgery, and a different invariant, the tree-part of the LMO invariant. Our method also constructs links with trivial higher Alexander modules and nontrivial Milnor invariants.
Keywords: Alexander module, claspers, Aarhus integral
Mots-clés : Milnor invariants, LMO invariant. 
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     author = {S. Garoufalidis},
     title = {Links with trivial {Alexander} module and nontrivial {Milnor} invariants},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {41--49},
     publisher = {mathdoc},
     number = {17},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a4/}
}
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S. Garoufalidis. Links with trivial Alexander module and nontrivial Milnor invariants. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 17 (2015), pp. 41-49. http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a4/