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Global homotopy theory
via partially lax limits
Sil Linskens, Denis Nardin and Luca Pol |
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Geometry & Topology 29 (2025) 1345–1440
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Abstract |
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We provide new -categorical models for unstable and stable global homotopy theory. We use the notion of partially lax limits to formalize the idea that a global object is a collection of -objects, one for each compact Lie group , which are compatible with the restriction–inflation functors. More precisely, we show that the -category of global spaces is equivalent to a partially lax limit of the functor sending a compact Lie group to the -category of -spaces. We also prove the stable version of this result, showing that the -category of global spectra is equivalent to the partially lax limit of a diagram of -spectra. Finally, the techniques employed in the previous cases allow us to describe the -category of proper -spectra for a Lie group , as a limit of a diagram of -spectra for running over all compact subgroups of . |
Keywords
partially lax limits, global homotopy theory, proper
equivariant homotopy theory
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Mathematical Subject Classification
Primary: 55N91, 55P91
Secondary: 18N70
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References |
Publication
Received: 22 June 2022
Revised: 5 March 2024
Accepted: 8 June 2024
Published: 31 May 2025
Proposed: Jesper Grodal
Seconded: Mark Behrens, Haynes R Miller
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Authors |
| Sil Linskens | |
| Fakultät für Mathematik Universität Regensburg Regensburg Germany |
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| Denis Nardin | |
| Fakultät für Mathematik Universität Regensburg Regensburg Germany |
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| Luca Pol | |
| Fakultät für Mathematik Universität Regensburg Regensburg Germany |
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| © 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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