A surgery formula for the 2loop piece of the LMO invariant of a pair
Abstract
Let \Theta (M,K) denote the 2loop 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2002
 arXiv:
 arXiv:math/0211057
 Bibcode:
 2002math.....11057K
 Keywords:

 Mathematics  Geometric Topology;
 57M27;
 57M25
 EPrint:
 Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper11.abs.html