A Geometric Model for Real and Complex Differential K-theory

<p>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.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2021

Author dc:creator

• Cushman, Matthew T

Advisor dc:contributor.advisor

• Scott Wilson

Committee members dc:contributor.committeemember

• Thomas Tradler
• Mahmoud Zeinalian

• Geometry and Topology
• differential geometry
• algebraic topology
• K-theory
• spin geometry
• Clifford algebras
• characteristic classes

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/4467

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-5551