Dissertations, Theses, and Capstone Projects
Date of Degree
9-2016
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
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.
Recommended Citation
Park, Byung Do, "A Geometric Model of Twisted Differential K-theory" (2016). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1533