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Twisted spectra
revisited
Alice Hedenlund and Tasos Moulinos |
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Algebraic & Geometric Topology 25 (2025) 5693–5754
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Abstract |
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We recapture Douglas’s framework for twisted parametrized stable homotopy theory in the language of -categories. A twisted spectrum is essentially a section of a bundle of presentable stable -categories whose fiber is the -category of spectra, a perspective we refine. We recover some of Douglas’s results on classifications of such bundles, as well as further make precise the identification of categories of twisted spectra with module categories over Thom spectra in the pointed connected case. Furthermore, we examine subtle aspects of the functoriality which arise by virtue of being fibered over the Brauer space of the sphere spectrum. Extending beyond the scope of Douglas’s work, we introduce a total category of twisted spectra over a fixed space, where we allow the twists to vary, and show that these total categories themselves satisfy the essential features of a 6-functor formalism. We also introduce an -category of twisted spectra, and use this framework to discuss duality theory for these types of objects. |
Keywords
stable homotopy theory, Floer homotopy theory, homotopical
algebra
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Mathematical Subject Classification
Primary: 18N60, 55P42, 57R58
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References |
Publication
Received: 25 November 2024
Accepted: 23 December 2024
Published: 18 December 2025
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Authors |
| Alice Hedenlund | |
| Uppsala University Uppsala Sweden |
Institutt for matematiske fag,
NTNU Norwegian University of Science and Technology Trondheim Norway |
| Tasos Moulinos | |
| Institute for Advanced Study Princeton, NJ United States |
Faculté des Sciences d’Orsay Université Paris-Saclay, CNRS Orsay France |
| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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