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Peer-reviewedCC BYJournal of Topology

Twisted ambidexterity in equivariant homotopy theory

  • Bastiaan Cnossen1
  1. 1Mathematisches Institut Universität Regensburg Regensburg Germany
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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.

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Cite

BibTeXRIS
BibTeX
@article{cnossen2026twisted,
  title = {{Twisted ambidexterity in equivariant homotopy theory}},
  author = {Bastiaan Cnossen},
  journal = {Journal of Topology},
  year = {2026},
  month = jun,
  doi = {10.1112/topo.70083},
  url = {https://doi.org/10.1112/topo.70083},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Twisted ambidexterity in equivariant homotopy theory
AU  - Bastiaan Cnossen
PY  - 2026
DA  - 2026/06/01
JO  - Journal of Topology
DO  - 10.1112/topo.70083
UR  - https://doi.org/10.1112/topo.70083
AB  - 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.
SN  - 1753-8416
SN  - 1753-8424
ER  -