Given a compact manifold and a smooth map from to the Lie group of unitary matrices with entries in , we construct a Chern character which lives in the odd part of the equivariant (entire) cyclic Chen-normalized cyclic complex of , and which is mapped to the odd Bismut–Chern character under the equivariant Chen integral map. It is also shown that the assignment induces a well-defined group homomorphism from the theory of to the odd homology group of .
Cite this article
Sergio L. Cacciatori, Batu Güneysu, Odd characteristic classes in entire cyclic homology and equivariant loop space homology. J. Noncommut. Geom. 15 (2021), no. 2, pp. 615–642DOI 10.4171/JNCG/406