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Finite type invariants of knots in homology 3-spheres with respect to null LP-surgeries
Delphine Moussardsubject
Pure mathematicsAlexander polynomialPrimary: 57M27Homology (mathematics)01 natural sciencesHomology sphereMathematics::Algebraic TopologyMathematics - Geometric TopologyKnot (unit)Mathematics::K-Theory and Homologybeaded Jacobi diagramknot[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics0101 mathematicsInvariant (mathematics)Mathematics::Symplectic Geometry3-manifoldhomology sphereMathematicsBorromean surgerycalculus010102 general mathematicsGeometric Topology (math.GT)Kontsevich integral16. Peace & justiceMathematics::Geometric TopologymanifoldsFinite type invariantnull-move57M27Finite type invariantLagrangian-preserving surgeryEquivariant map010307 mathematical physicsGeometry and Topology3-manifolddescription
We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial description of the graded space associated with our theory and determine some cases when this description is complete. For null-homologous knots in rational homology 3-spheres with a trivial Alexander polynomial, we show that the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant built from integrals in configuration spaces are universal finite type invariants for this theory; in particular it implies that they are equivalent for such knots.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-10-23 |