A surgery view of boundary links

Details A surgery view of boundary links A surgery view of boundary links

2002-05-31

arxiv.org/abs/math/0205328v2

Mathematics

Geometric Topology

LaTeX, 8 pages with 5 figures

Scientific paper

A celebrated theorem of Kirby identifies the set of closed oriented connected 3-manifolds with the set of framed links in $S^3$ modulo two moves. We give a similar description for the set of knots (and more generally, boundary links) in homology 3-spheres. As an application, we define a noncommutative version of the Alexander polynomial of a boundary link. Our surgery view of boundary links is a key ingredient in a construction of a rational version of the Kontsevich integral, which is described in subsequent work. The current version fixes minor typographical errors.

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