Homotopy Representations and the Picard Group of the Equivariant Stable Homotopy Category

Erik Knutsen

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arXiv · 2311.11915

Homotopy Representations and the Picard Group of the Equivariant Stable Homotopy Category

Erik Knutsen

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Abstract

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism when $G$ is a compact Lie group with component group $\Gamma$ having the property that all projective $\mathbb{Z}\Gamma$-modules are stably free. This resolves a conjecture of Fausk, Lewis, and May for such $G$, giving a better description of the Picard group of the homotopy category of $G$-spectra.

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BibTeX RIS

Erik Knutsen. 2023-11-20. Homotopy Representations and the Picard Group of the Equivariant Stable Homotopy Category. https://arxiv.org/abs/2311.11915

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