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Noncommutative differential K-theory

by Byungdo Park, Arthur J. Parzygnat, Corbett Redden, Augusto Stoffel




Journal of Geometry and Physics, Volume 174, article id. 104446.


We introduce a differential extension of algebraic K-theory of an algebra using Karoubi's Chern character. In doing so, we develop a necessary theory of secondary transgression forms as well as a differential refinement of the smooth Serre--Swan correspondence. Our construction subsumes the differential K-theory of a smooth manifold when the algebra is complex-valued smooth functions.


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Additional Information

Brief introduction of the dida co-author(s) and relevance for dida's ML developments.

About the Co-Author

Augusto studied computer engineering in Brazil and holds a PhD in mathematics (University of Notre Dame, USA). Before joining dida, he was a postdoc in Bonn and Greifswald, doing research in the field of algebraic topology and its application as a foundation of quantum field theory.