Links with trivial Alexander module and nontrivial Milnor invariants

Details Links with trivial Alexander module and nontrivial Milnor invariants Links with trivial Alexander module and nontrivial Milnor invariants

2002-06-19

arxiv.org/abs/math/0206196v2

Mathematics

Geometric Topology

LaTeX, 6 pages with 8 figures

Scientific paper

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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