The Dixmier-Douady class in the Simplicial de Rham Complex

TL;DR

This paper constructs a cocycle in the simplicial de Rham complex that explicitly represents the Dixmier-Douady class, building on prior work by Carey, Crowley, and Murray.

Contribution

It provides an explicit cocycle in the simplicial de Rham complex representing the Dixmier-Douady class, advancing the understanding of its geometric and algebraic properties.

Findings

Explicit cocycle construction in simplicial de Rham complex

Representation of the Dixmier-Douady class

Extension of previous theoretical frameworks

Abstract

On the basis of A. L. Carey, D. Crowley, M. K. Murray's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Dixmier-Douady class.