Motivic Milnor fiber of cyclic L-infinity algebras

Abstract

We define motivic Milnor fiber of cyclic $L_\infty$-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the \'{e}tale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by $L$ is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that Behrend function depends only on the formal neighborhood of the moduli space.