2026/02/27 by Taesu Kim, Yong-Geun Oh · 1 voice · 1 citation
Mathematics · #math.SG #math.DG
Jae-Suk Park and the second-named author introduce the deformation problem of coisotropic submanifolds of a symplectic manifold as the study of Mauer-Cartan moduli problem of an L_∞ algebra attached to the foliation de-Rham complex associated to the null foliation of the corresponding presymplectic structure. The main purpose of the present paper is to extend this study of L_∞ structures to the case of generic closed two-forms on arbitrary smooth manifolds as a stratified L_∞ space. We first prove that there exists a residual subset of closed 2-forms, which we denote by Z2reg(M) ⊂ Z2(M), such that any element ω therefrom admits a Whitney stratification each of whose strata is a presymplectic manifold. We then associate an L_∞ space to each stratum (and to its tubular neighborhood) and glue the collection of L_∞ spaces to a global stratified L_∞ space by the coordinate atlas consisting of L_∞ morphisms, which is a collection of L_∞ morphisms, not necessarily of quasi-isomorphisms.