Twisted ambidexterity in equivariant homotopy theory
Year: 2026
Type: article
Abstract: We develop the concept of twisted ambidexterity in a parametrized presentably symmetric monoidal ‐category, which generalizes the notion of ambidexterity by Hopkins and Lurie and the Wirthmüller isomorphisms in equivariant stable homotopy theory, and is closely related to Costenoble–Waner duality. Our main result establishes the parametrized ‐category of genuine ‐spectra for a compact Lie group as the universal example of a presentably symmetric monoidal ‐category parametrized over ‐spaces which is both stable and satisfies twisted ambidexterity for compact ‐spaces. We further extend this result to the settings of equivariant spectra over orbispaces and proper genuine equivariant spectra.
Source: Journal of Topology
DOI: 10.1112/topo.70083
Author: Bastiaan Cnossen
Institution: University of Regensburg
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,930
OpenAlex ID: W4322825209