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arXiv · 2406.13212

A Comparison of Takai and Treumann Dualities

Vikram Nadig
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Abstract

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

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Vikram Nadig. 2024-06-19. A Comparison of Takai and Treumann Dualities. https://doi.org/10.2140/akt.2025.10.563

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