Volume 20, issue 1 (2020)

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Splitting formulas for the rational lift of the Kontsevich integral

Delphine Moussard

Algebraic & Geometric Topology 20 (2020) 303–342
Abstract

Kricker defined an invariant of knots in homology $3$–spheres which is a rational lift of the Kontsevich integral and proved with Garoufalidis that this invariant satisfies splitting formulas with respect to a surgery move called null-move. We define a functorial extension of the Kricker invariant and prove splitting formulas for this functorial invariant with respect to null Lagrangian-preserving surgery, a generalization of the null-move. We apply these splitting formulas to the Kricker invariant.

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Keywords
$3$–manifold, knot, homology sphere, cobordism category, Lagrangian cobordism, bottom–top tangle, beaded Jacobi diagram, Kontsevich integral, LMO invariant, Kricker invariant, Lagrangian-preserving surgery, finite type invariant, splitting formula
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25, 57N10
Publication
Received: 9 September 2018
Revised: 4 February 2019
Accepted: 24 February 2019
Published: 23 February 2020
Authors
 Delphine Moussard Japan Society for the Promotion of Science Research Institute for Mathematical Sciences Kyoto University Kyoto Japan Institut de Mathématiques de Marseille Aix-Marseille University Marseille France