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Links with trivial Alexander module and nontrivial Milnor invariants

Stavros Garoufalidis
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Abstract

Minor typographical errors fixed. 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.

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Stavros Garoufalidis. 2002-07-08. Links with trivial Alexander module and nontrivial Milnor invariants. https://arxiv.org/abs/math/0206196

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