Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 11, pages 161--181.

A surgery formula for the 2-loop piece of the LMO invariant of a pair

Andrew Kricker

Abstract. Let \Theta (M,K) denote the 2-loop piece of (the logarithm of) the LMO invariant of a knot K in M, a ZHS^3. Forgetting the knot (by which we mean setting diagrams with legs to zero) specialises \Theta (M,K) to \lambda (M), Casson's invariant. This note describes an extension of Casson's surgery formula for his invariant to \Theta (M,K). To be precise, we describe the effect on \Theta (M,K) of a surgery on a knot which together with K forms a boundary link in M. Whilst the presented formula does not characterise \Theta (M,K), it does allow some insight into the underlying topology.

Keywords. Casson's invariant, LMO invariant, boundary link, surgery

AMS subject classification. Primary: 57M27. Secondary: 57M25.

E-print: arXiv:math.GT/0211057

Submitted to GT on 19 December 2001. (Revised 6 August 2002.) Paper accepted 10 September 2002. Paper published 21 September 2002.

Notes on file formats

Andrew Kricker
Department of Mathematics, University of Toronto
Ontario, M5S 1A1, Canada

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