Algebraic K-theory breaks into two pieces: nil if-theory and Karoubi-Villamayor K-theory. Karoubi has constructed Chern classes from the latter groups into cyclic homology. We construct maps from nil if-theory to cyclic homology which are compatible with Karoubi’s maps, but with a degree shift. Several recent results show that in characteristic zero our map is often an isomorphism.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Algebraic K-theory. Partially supported by NSF grant
- Cyclic homology