A Comparison of Takai and Treumann Dualities

Abstract

We prove a comparison result between two duality statements - Takai duality, which is implemented by the crossed product functor $-⋊G:K{K}^G\to K{K}^{\hat{G}}$ on equivariant Kasparov categories; and Treumann duality, which asserts the existence of an exotic equivalence of stable $\infty$-categories $\text{Mod}(K{U}_p[G]{)}^{ft}\simeq \text{Mod}(K{U}_p[\hat{G}]{)}^{ft}$ given by tensoring with a particular $(G,\hat{G})$-bimodule $\text{M}$.

34 pages; accepted version, to appear in the Annals of K-Theory

References in corpus (1)

• KK- and E-theory via homotopy theory