Algebraic kk-theory and the KH-isomorphism conjecture

TL;DR

This paper connects Davis-Lück homology with Weibel's homotopy K-theory to equivariant algebraic kk-theory, providing a new perspective on the KH-isomorphism conjecture using homotopy theory.

Contribution

It introduces a novel relationship between Davis-Lück homology and equivariant algebraic kk-theory, advancing understanding of the KH-isomorphism conjecture.

Findings

Expresses the assembly map for the KH-conjecture in terms of equivariant algebraic kk-groups.

Relates homology theories with algebraic kk-theory using homotopy-theoretic methods.

Provides a new framework for analyzing the KH-isomorphism conjecture.

Abstract

We relate the Davis-L\"uck 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.