Finite type invariants of knots in homology 3-spheres with respect to null LP-surgeries

Delphine Moussard (1, 2)

1 JSPS - Japan Society for the Promotion of Science
2 Research Institute for Mathematical Sciences

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.

Mots clés: Finite type invariant; Lagrangian-preserving surgery; null-move; Borromean surgery; Kontsevich integral; 3-manifold; knot; homology sphere; beaded Jacobi diagram

Domaines: Topologie géométrique [math.GT]

Delphine Moussard. Finite type invariants of knots in homology 3-spheres with respect to null LP-surgeries. Geometry and Topology, 2019. ⟨hal-01620930v2⟩