$L_{\infty}$-Kuranishi spaces and the moduli space of pseudoholomorphic disks

Abstract

We show that the moduli space of pseudoholomorphic disks is an example of the $L_{\infty}$-Kuranishi spaces introduced in \cite{Kim1}, provided that a condition for the existence of a stratification with a system of tubular neighborhoods holds on each chart. With respect to this structure, the forgetful and evaluation maps for the moduli space lift to morphisms between $L_{\infty}$-Kuranishi spaces.