The Thom-Sebastiani theorem for the Euler characteristic of cyclic L∞-algebras

In this paper we prove a Thom-Sebastiani type formula for the Euler characteristic of cyclic L∞-algebras. As applications we prove the Joyce-Song formulas about the Behrend function identities for semi-Schur objects in the derived category of coherent sheaves over Calabi-Yau threefolds. A motivic Thom-Sebastiani type formula and a conjectural motivic Joyce-Song formula for the motivic Milnor fiber of cyclic L∞-algebras are also discussed.