Twisted K-theory and K-theory of bundle gerbes

TL;DR

This work develops bundle gerbe K-theory and clarifies its precise relationship to twisted K-theory. By introducing bundle gerbe modules, the authors construct a K-theory for bundle gerbes that matches twisted K-theory when the Dixmier–Douady class is torsion, and extend the framework to non-torsion via lifting bundle gerbes and U_K-bundle gerbe modules, yielding a robust bridge to twisted cohomology. They establish a Chern character for twisted K-theory through bundle gerbe connections and curvings, linking twisted K-theory to twisted cohomology in both torsion and non-torsion contexts. A suite of explicit 3-manifold examples demonstrates the computational power of the approach and illuminates the interplay between topology, geometry of gerbes, and D-brane charge classifications in string theory. The results provide a coherent geometric and algebraic toolkit for analyzing D-brane charges in nontrivial B-field backgrounds and offer a foundation for future applications in string/M-theory and noncommutative geometry.

Abstract

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed.

Theorems & Definitions (24)

• Theorem 2.1: Mur
• Theorem 2.2: Mur
• Definition 3.1
• Proposition 3.2
• Theorem 3.3
• Proposition 4.1
• Proposition 4.2
• Proposition 4.3
• Proposition 4.4
• Proposition 5.1