Date of Degree

9-2021

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Scott Wilson

Committee Members

Thomas Tradler

Mahmoud Zeinalian

Subject Categories

Geometry and Topology

Keywords

differential geometry, algebraic topology, K-theory, spin geometry, Clifford algebras, characteristic classes

Abstract

We construct a differential-geometric model for real and complex differential K-theory based on a smooth manifold model for the K-theory spectra defined by Behrens using spaces of Clifford module extensions. After writing representative differential forms for the universal Pontryagin and Chern characters we transgress these forms to all the spaces of the spectra and use them to define an abelian group structure on maps up to an equivalence relation that refines homotopy. Finally we define the differential K-theory functors and verify the axioms of Bunke-Schick for a differential cohomology theory.

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