2019/06/06 by Kowshik Bettadapura, Bettadapura, Kowshik
Mathematics · #14H15 #32C11 #55N30 #58A50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1906.02391
openalex publication_date 2019/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study the notion of supermanifolds families, starting from Green's general classification of supermanifolds. The topics studied divide this article into two distinct parts, labelled I and II respectively. Part I concerns the splitting type of a supermanifold and our attempt to construct variations thereof. In Part II we look at a particular class of families, referred to as `gtm-families'. We are concerned with the notion of a `secondary obstruction theory', which is apparent in any gtm-family of supermanifolds over a (connected and Stein) non-reduced, superspace base.