2023/12/20 by Cristian Camilo Cárdenas, Cárdenas, Cristian Camilo
Mathematics · #22A22 #53D17 #54C35 (Secondary) #58H15 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2312.12762
openalex publication_date 2023/12/20 · openalex created_date 2023/12/22 · openalex updated_date 2026/07/28
We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally, we establish stability properties of the morphisms using Moser-type arguments. Furthermore, we demonstrate the Morita invariance of the deformation cohomology and consider simultaneous deformations of the morphism, its domain, and codomain. These simultaneous deformations are utilized to define cohomology for generalized morphisms and to study deformations of multiplicative forms on Lie groupoids.