Differential forms on diffeological spaces and diffeological gluing, I

2016/05/24 by Pervova, Ekaterina
#53C15 (primary) #57R35 #57R45 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.07328

Abstract

This paper aims to describe the behavior of diffeological differential forms under the operation of gluing of diffeological spaces along a smooth map. In the diffeological context, two ways of looking at diffeological forms are available, that of the vector space of all diffeological forms on a given space, and that of the pseudo-bundle of values of these forms. We describe the behavior of the former under a gluing of diffeological spaces.

Related

• Diffeological connections on diffeological vector pseudo-bundles
• Diffeological gluing of vector pseudo-bundles and pseudo-metrics on them
• Diffeological, Frölicher, and Differential Spaces
• Exterior bundles in diffeology
• Diffeologies, Differential Spaces, and Symplectic Geometry