2016/01/30 by Junwu Tu, Tu, Junwu
Mathematics · #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #math.SG #msc:53D30 #msc:58A05
paper · pdf · doi:10.48550/arxiv.1602.00150
comments welcome!
arxiv created 2016/01/30 · arxiv updated 2016/02/02
Motivated by the definition of homotopy L_∞ spaces, we develop a new theory of Kuranishi manifolds, closely related to Joyce's recent theory. We prove that Kuranishi manifolds form a 2-category with invertible 2-morphisms, and that certain fiber product property holds in this 2-category. In a subsequent paper, we construct the virtual fundamental cycle of a compact oriented Kuranishi manifold, and prove some of its basic properties. Manifest from this new formulation is the fact that [0,1]-type homotopy L_∞ spaces are naturally Kuranishi manifolds. The former structured spaces naturally appear as derived enhancements of Maurer-Cartan moduli spaces from Chern-Simons type gauge theory. In this way, Kuranishi manifolds theory can be applied to study path integrals in such type of gauge theories.