Algebraic $kk$-theory and the KH-isomorphism conjecture

Eugenia Ellis; Emanuel Rodríguez Cirone

doi:10.4171/dm/953

JournalsdmVol. 29, No. 2pp. 399–456

Algebraic $kk$ -theory and the KH-isomorphism conjecture

Eugenia Ellis
Universidad de la República, Montevideo, Uruguay
Emanuel Rodríguez Cirone
Universidad de Buenos Aires, Buenos Aires, Argentina

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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.

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Eugenia Ellis, Emanuel Rodríguez Cirone, Algebraic $kk$ -theory and the KH-isomorphism conjecture. Doc. Math. 29 (2024), no. 2, pp. 399–456

DOI 10.4171/DM/953