Abstract
The Segal conjecture describes stable maps between classifying spaces in terms of (virtual) bisets for the finite groups in question. Along these lines, we give an algebraic formula for the p-completion functor applied to stable maps between classifying spaces purely in terms of fusion data and Burnside modules.
Original language | American English |
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Article number | 108255 |
Journal | Topology and its Applications |
Volume | 322 |
DOIs | |
State | Published - 1 Dec 2022 |
Bibliographical note
Funding Information:All three authors would like to thank the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics for their hospitality and support. While working on this paper the first author was funded by the Independent Research Fund Denmark ( DFF–4002-00224 ) and later on by BGSMath and the María de Maeztu Programme ( MDM–2014-0445 ). The second and third author were jointly supported by the US-Israel Binational Science Foundation under grant 2018389 . The second author was partially supported by the Alon Fellowship and ISF 1588/18 . The third author was partially supported by NSF grant DMS-1906236 and the SFB 1085 Higher Invariants at the University of Regensburg . The first author would like to thank his working group at HIM for being patient listeners to discussions about bisets, I-adic topologies, and p-completions.
Funding Information:
All three authors would like to thank the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics for their hospitality and support. While working on this paper the first author was funded by the Independent Research Fund Denmark (DFF–4002-00224) and later on by BGSMath and the María de Maeztu Programme (MDM–2014-0445). The second and third author were jointly supported by the US-Israel Binational Science Foundation under grant 2018389. The second author was partially supported by the Alon Fellowship and ISF 1588/18. The third author was partially supported by NSF grant DMS-1906236 and the SFB 1085 Higher Invariants at the University of Regensburg. The first author would like to thank his working group at HIM for being patient listeners to discussions about bisets, I-adic topologies, and p-completions.
Publisher Copyright:
© 2022 Elsevier B.V.
Keywords
- Burnside ring
- Fusion systems
- Segal conjecture
- Spectra
- p-completion