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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Cushman, Matthew T"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Scott Wilson"],"committee_chairs":[],"committee_members":["Thomas Tradler","Mahmoud Zeinalian"],"year":2021,"date_issued":"2021-09-01T07:00:00Z","date_published":"2021-09-01T07:00:00Z","updated_at":"2026-07-24T01:58:31Z","subjects":["Geometry and Topology","differential geometry","algebraic topology","K-theory","spin geometry","Clifford algebras","characteristic classes"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/4467","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Scott Wilson"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Thomas Tradler","Mahmoud Zeinalian"]},{"key":"dc:creator","label":"Author","values":["Cushman, Matthew T"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2021-08-03T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Geometry and Topology","differential geometry","algebraic topology","K-theory","spin geometry","Clifford algebras","characteristic classes"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/4467"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["A Geometric Model for Real and Complex Differential K-theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Scott Wilson"],"dc:contributor.committeemember":["Thomas Tradler","Mahmoud Zeinalian"],"dc:creator":["Cushman, Matthew T"],"dc:date.available":["2021-08-03T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/4467"],"dc:subject":["Geometry and Topology","differential geometry","algebraic topology","K-theory","spin geometry","Clifford algebras","characteristic classes"],"dc:title":["A Geometric Model for Real and Complex Differential K-theory"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T01:58:31Z"}