A comparison of Takai and Treumann dualities

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

Fun (B G, Perf (K U_{p})) ≃ Fun (B \hat{G}, Perf (K U_{p}))

given by tensoring with a particular $(G, \hat{G})$ -bimodule $M$ .

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Keywords

$KK$-theory, Takai duality, Treumann duality

Mathematical Subject Classification

Primary: 19K35, 19L47

Secondary: 55P43

Milestones

Received: 24 October 2024

Revised: 12 August 2025

Accepted: 29 August 2025

Published: 6 October 2025

Authors

Vikram Nadig
Universität Bielefeld Bielefeld Germany

Vol. 10, No. 3, 2025

Vikram Nadig

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors