Geometry and Topology

Links with trivial Alexander module and nontrivial Milnor invariants

S. Garoufalidis

School of Mathematics of Georgia Institute of Technology, Atlanta, USA

Abstract: 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, Milnor invariants, claspers, Aarhus integral, LMO invariant.

UDC: 515.163
BBK: B151.5

Language: English