A version of smooth K-theory adapted to the total Chern class
Alain Berthomieu
TL;DR
This paper develops a new version of smooth K-theory tailored to the total Chern class, providing a morphism to Cheeger-Simons differential characters, thus addressing an open question in the field.
Contribution
It introduces a novel smooth K-theory framework based on the total Chern class, differing from previous theories that focused on the Chern character.
Findings
Constructed a smooth K-theory adapted to the total Chern class
Established a total Chern class morphism to Cheeger-Simons differential characters
Answered an open question by U. Bunke
Abstract
A version of smooth K-theory is constructed, which is adapted to the total Chern class instead of the Chern character (contrarily to previous theories). Some total Chern class morphism from this K-theory to Cheeger-Simons differential characters is constructed. This answers a question raised by U. Bunke.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research · Algebraic structures and combinatorial models