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A surgery view of boundary links

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Abstract.

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.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA

    Stavros Garoufalidis

  2. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 3G3

    Andrew Kricker

Authors
  1. Stavros Garoufalidis
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  2. Andrew Kricker
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Corresponding author

Correspondence to Stavros Garoufalidis.

Additional information

Mathematics Subject Classification (1991): 57N10, 57M25

S.G. was partially supported by an NSF grant DMS-02-03129 and by an Israel-US BSF grant.

A.K. was supported by an Israel Fellowship.

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Garoufalidis, S., Kricker, A. A surgery view of boundary links. Math. Ann. 327, 103–115 (2003). https://doi.org/10.1007/s00208-003-0434-9

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  • DOI: https://doi.org/10.1007/s00208-003-0434-9

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