Families of Supermanifolds: Splitting Types and Obstruction Maps

Abstract

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.