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

Mathematics

Producción científica: Article › revisión exhaustiva

Resumen

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.

Idioma original	English
Número de artículo	108255
Publicación	Topology and its Applications
Volumen	322
DOI	https://doi.org/10.1016/j.topol.2022.108255
Estado	Published - dic 1 2022

Nota bibliográfica

Publisher Copyright:
© 2022 Elsevier B.V.

Financiación

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. 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.

Financiadores	Número del financiador
Alon Fellowship	ISF 1588/18
María de Maeztu Programme	MDM–2014-0445
National Science Foundation Arctic Social Science Program	DMS-1906236
United States-Israel Binational Science Foundation	2018389
Universität Regensburg
Danmarks Frie Forskningsfond	DFF–4002-00224
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Hausdorff Research Institute for Mathematics

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2022.108255

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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.",

keywords = "Burnside ring, Fusion systems, Segal conjecture, Spectra, p-completion",

author = "Reeh, \{Sune Precht\} and Schlank, \{Tomer M.\} and Nathaniel Stapleton",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

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day = "1",

doi = "10.1016/j.topol.2022.108255",

language = "English",

volume = "322",

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T1 - A formula for p-completion by way of the Segal conjecture

AU - Reeh, Sune Precht

AU - Schlank, Tomer M.

AU - Stapleton, Nathaniel

PY - 2022/12/1

Y1 - 2022/12/1

N2 - 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.

AB - 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.

KW - Burnside ring

KW - Fusion systems

KW - Segal conjecture

KW - Spectra

KW - p-completion

UR - https://www.scopus.com/pages/publications/85139738720

UR - https://www.scopus.com/pages/publications/85139738720#tab=citedBy

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DO - 10.1016/j.topol.2022.108255

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SN - 0166-8641

VL - 322

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 108255

ER -

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

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