Algebraic kk-theory and the KH-isomorphism conjecture
Abstract
We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for the KH-isomorphism conjecture in terms of equivariant algebraic kk-groups.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2022
- DOI:
- 10.48550/arXiv.2205.04558
- arXiv:
- arXiv:2205.04558
- Bibcode:
- 2022arXiv220504558E
- Keywords:
-
- Mathematics - K-Theory and Homology;
- Mathematics - Algebraic Topology;
- 19D55 (primary) 55N91;
- 18N40;
- 19K35 (secondary)
- E-Print:
- 47 pages. The introduction was completely rewritten. Two sections were added: section 2 with preliminaries and section 8 on defining a kk-theoretic assembly map for KH