A formula for p-completion by way of the Segal conjecture

Sune Precht Reeh; Tomer M. Schlank; Nathaniel Stapleton

doi:10.1016/j.topol.2022.108255

A formula for p-completion by way of the Segal conjecture

Sune Precht Reeh, Tomer M. Schlank, Nathaniel Stapleton^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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
Article number	108255
Journal	Topology and its Applications
Volume	322
DOIs	https://doi.org/10.1016/j.topol.2022.108255
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

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title = "A formula for p-completion by way of the Segal conjecture",

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.",

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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 Mar{\'i}a 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 Mar{\'i}a 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: {\textcopyright} 2022 Elsevier B.V.",

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A formula for p-completion by way of the Segal conjecture

Abstract

Bibliographical note

Keywords

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