Gerbes, Holonomy Forms and Real Structures

TL;DR

This paper explores the geometry of real gerbes, introducing holonomy forms and adaptations, and examines their relations to complex gerbes, with applications to loop and map spaces.

Contribution

It introduces the concepts of adaptations and holonomy forms for flat connections on real gerbes and relates them to complex gerbes, expanding geometric understanding.

Findings

Defined holonomy forms for real gerbes

Established relations between real and complex gerbes

Applied concepts to loop and map spaces

Abstract

We study geometry on real gerbes in the spirit of Cheeger-Simons theory. The concepts of adaptations and holonomy forms are introduced for flat connections on real gerbes. Their relations to complex gerbes with connections are presented, as well as results in loop and map spaces.