Twisted ambidexterity in equivariant homotopy theory
Abstract
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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Publication details
- Journal / source
- Journal of Topology
- Publisher
- Wiley
- Volume
- 19
- Issue
- 2
- Publication date
- 1 June 2026
- Language
- EN