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

Andrew Kricker

Geometry & Topology Monographs 4 (2002) 161–181

DOI: 10.2140/gtm.2002.4.161

Abstract

Let Θ(M,K) denote the 2–loop piece of (the logarithm of) the LMO invariant of a knot K in M, a ZHS3. Forgetting the knot (by which we mean setting diagrams with legs to zero) specialises Θ(M,K) to λ(M), Casson's invariant. This note describes an extension of Casson's surgery formula for his invariant to Θ(M,K). To be precise, we describe the effect on Θ(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 Θ(M,K), it does allow some insight into the underlying topology.

Keywords

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

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M25

References
Publication

Received: 19 December 2001
Revised: 6 August 2002
Accepted: 10 September 2002
Published: 21 September 2002

Authors
Andrew Kricker