2023/07/17 by Behrend, Kai, Liao, Hsuan-Yi, Xu, Ping · 1 citation
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2307.10242
We prove that dg manifolds of finite positive amplitude, i.e. bundles of positively graded curved L_∞[1]-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces. First we construct an infinite-dimensional factorization of a diagonal morphism using actual path spaces motivated by the AKSZ construction. Then we cut down to finite dimensions using the Fiorenza-Manetti method. The main ingredient in our method is the homotopy transfer theorem for curved L_∞[1]-algebras. As an application, we study the derived intersections of manifolds.