A splicing formula for the LMO invariant - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Canadian Journal of Mathematics = Journal Canadien de Mathématiques Année : 2021

A splicing formula for the LMO invariant

Résumé

We prove a "splicing formula" for the LMO invariant, which is the universal finite-type invariant of rational homology $3$-spheres. Specifically, if a rational homology $3$-sphere $M$ is obtained by gluing the exteriors of two framed knots $K_1 \subset M_1$ and $K_2\subset M_2$ in rational homology $3$-spheres, our formula expresses the LMO invariant of $M$ in terms of the Kontsevich-LMO invariants of $(M_1,K_1)$ and $(M_2,K_2)$. The proof uses the techniques that Bar-Natan and Lawrence developed to obtain a rational surgery formula for the LMO invariant. In low degrees, we recover Fujita's formula for the Casson-Walker invariant and we observe that the second term of the Ohtsuki series is not additive under "standard" splicing. The splicing formula also works when each $M_i$ comes with a link $L_i$ in addition to the knot $K_i$, hence we get a "satellite formula" for the Kontsevich-LMO invariant.

Dates et versions

hal-02436372 , version 1 (13-01-2020)

Identifiants

Citer

Gwénaël Massuyeau, Delphine Moussard. A splicing formula for the LMO invariant. Canadian Journal of Mathematics = Journal Canadien de Mathématiques, 2021, 73 (6), pp.1743-1770. ⟨10.4153/S0008414X20000668⟩. ⟨hal-02436372⟩
75 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More