A splicing formula for the LMO invariant

We prove a ``splicing formula'' for the LMO invariant, which is the universal finite-type invariant of rational homology three-spheres. Specifically, if a rational homology three-sphere M is obtained by gluing the exteriors of two framed knots K-1 subset of M-1 and K-2 subset of M-2 in rational homology three-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.