Segal's conjecture and the Burnside rings of fusion systems

Antonio Diaz, Assaf Libman

Research output: Contribution to journalArticle

4 Citations (Scopus)
4 Downloads (Pure)

Abstract

For a given saturated fusion system F we define the ring A(S)^F of the F-invariants of the Burnside ring functor. We show how this ring is related to the Burnside ring of the fusion system F and how it appears naturally in the analogue of Segal's conjecture for the classifying spectrum ¿F. We give an explicit description of A(S)^F and we prove it is a local ring.
Original languageEnglish
Pages (from-to)665–679
Number of pages15
JournalJournal of the London Mathematical Society
Volume80
Issue number3
Early online date16 Sep 2009
DOIs
Publication statusPublished - Dec 2009

Fingerprint

Burnside Ring
Fusion
Ring
Local Ring
Functor
Analogue
Invariant

Keywords

  • fusion systems
  • Burnside ring

Cite this

Segal's conjecture and the Burnside rings of fusion systems. / Diaz, Antonio; Libman, Assaf.

In: Journal of the London Mathematical Society, Vol. 80, No. 3, 12.2009, p. 665–679.

Research output: Contribution to journalArticle

@article{07c21d93d8964089998b3fe4b2af2e3b,
title = "Segal's conjecture and the Burnside rings of fusion systems",
abstract = "For a given saturated fusion system F we define the ring A(S)^F of the F-invariants of the Burnside ring functor. We show how this ring is related to the Burnside ring of the fusion system F and how it appears naturally in the analogue of Segal's conjecture for the classifying spectrum ¿F. We give an explicit description of A(S)^F and we prove it is a local ring.",
keywords = "fusion systems, Burnside ring",
author = "Antonio Diaz and Assaf Libman",
year = "2009",
month = "12",
doi = "10.1112/jlms/jdp048",
language = "English",
volume = "80",
pages = "665–679",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "3",

}

TY - JOUR

T1 - Segal's conjecture and the Burnside rings of fusion systems

AU - Diaz, Antonio

AU - Libman, Assaf

PY - 2009/12

Y1 - 2009/12

N2 - For a given saturated fusion system F we define the ring A(S)^F of the F-invariants of the Burnside ring functor. We show how this ring is related to the Burnside ring of the fusion system F and how it appears naturally in the analogue of Segal's conjecture for the classifying spectrum ¿F. We give an explicit description of A(S)^F and we prove it is a local ring.

AB - For a given saturated fusion system F we define the ring A(S)^F of the F-invariants of the Burnside ring functor. We show how this ring is related to the Burnside ring of the fusion system F and how it appears naturally in the analogue of Segal's conjecture for the classifying spectrum ¿F. We give an explicit description of A(S)^F and we prove it is a local ring.

KW - fusion systems

KW - Burnside ring

U2 - 10.1112/jlms/jdp048

DO - 10.1112/jlms/jdp048

M3 - Article

VL - 80

SP - 665

EP - 679

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 3

ER -