Transgressing the algebraic coarse character map
Alexander Engel, Matthias Ludewig

TL;DR
This paper investigates a conjecture relating the algebraic K-theory of finite propagation operators to the Higson corona, showing that the algebraic coarse character map transgresses to the classical Chern character.
Contribution
It proves that transgressing the algebraic coarse character map on finite propagation operators aligns with the Chern character on the Higson corona, confirming a conjecture of John Roe.
Findings
Confirmed the conjecture relating algebraic K-theory and the Chern character.
Established the transgression of the algebraic coarse character map to the Higson corona.
Connected algebraic K-theory with classical topological invariants.
Abstract
We pursue an old conjecture of John Roe about the algebraic K-theory of the algebra of finite propagation, locally trace-class operators, namely that transgressing the algebraic coarse character map on this algebra to a Higson dominated corona coincides with the usual Chern character on the corona.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics, Computing, and Information Processing
