Date of Degree

9-2016

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor(s)

Mahmoud Zeinalian

Committee Members

Thomas Tradler

Scott Wilson

Corbett Redden

Subject Categories

Geometry and Topology

Keywords

Twisted K-theory, Differential K-theory, Twisted Chern Character, de Rham theorem

Abstract

We construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. We use smooth U(1)-gerbes with connection as differential twists and twisted vector bundles with connection as cycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. We also construct an odd twisted Chern character of a twisted vector bundle with an automorphism. In addition to our geometric model of twisted differential K-theory, we introduce a smooth variant of the Hopkins-Singer model of differential K-theory. We prove that our model is naturally isomorphic to the Hopkins-Singer model and also to the Tradler-Wilson-Zeinalian model of differential K-theory.

 
 

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