Algebraic kk-theory and the KH-isomorphism conjecture

2022/05/09 by Ellis, Eugenia, Cirone, Emanuel Rodríguez
#18N40 #19D55 (primary) 55N91 #19K35 (secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2205.04558

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.

Related

• The KH-Isomorphism Conjecture and Algebraic KK-theory
• Equivariant stable homotopy methods in the algebraic K-theory of infinite groups
• A kind of KK-theory for rings
• Equivariant Algebraic K-Theories
• C*-categories, Groupoid Actions, Equivariant KK-theory, and the Baum-Connes Conjecture