Twisted ambidexterity in equivariant homotopy theory

Autor:	Cnossen, Bastiaan
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Topology
Druh dokumentu:	Working Paper
Popis:	We develop the concept of twisted ambidexterity in a parametrized presentably symmetric monoidal $\infty$-category, which generalizes the notion of ambidexterity by Hopkins and Lurie and the Wirthm\"uller isomorphisms in equivariant stable homotopy theory, and is closely related to Costenoble-Waner duality. Our main result establishes the parametrized $\infty$-category of genuine $G$-spectra for a compact Lie group $G$ as the universal example of a presentably symmetric monoidal $\infty$-category parametrized over $G$-spaces which is both stable and satisfies twisted ambidexterity for compact $G$-spaces. We further extend this result to the settings of orbispectra and proper genuine $G$-spectra for a Lie group $G$ which is not necessarily compact. Comment: Comments welcome! v2: corrected typos, added reference to Quigley-Shah
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.00736 Zobrazit plný text záznamu View this record from Arxiv