Normalizers of chains of discrete p-toral subgroups in compact Lie groups
Normalizers of chains of discrete p-toral subgroups in compact Lie groups
In this paper we study the normalizer decomposition of a compact Lie group G using the information of the fusion system F of G on a maximal discrete p-toral subgroup. We prove that there is an injective map from the set of conjugacy classes of chains of F-centric, F-radical discrete p-toral subgroups to the set of conjugacy classes of chains of p-centric, p-stubborn continuous p-toral subgroups. The map is a bijection when π0(G) is a finite p-group. We also prove that the classifying space of the normalizer of a chain of discrete p-toral subgroups of G is mod p equivalent to the classifying space of the normalizer of the corresponding chain of p-toral subgroups.
Classifying spaces, Compact Lie groups, Fusion, p-completion
1-18
Belmont, Eva
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Castellana, Natàlia
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Grbić, Jelena
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Lesh, Kathryn
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Strumila, Michelle
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1 July 2022
Belmont, Eva
10b1fc14-47b0-468f-a597-4f2727ef66cc
Castellana, Natàlia
f0cbb6cf-d4d0-4fba-a979-864b3f46bb7d
Grbić, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Lesh, Kathryn
3c7c0119-f0fe-4b0e-adb7-fd56646d1df1
Strumila, Michelle
a4f5390d-9569-4f3f-ba1f-bbe139549ca4
Belmont, Eva, Castellana, Natàlia, Grbić, Jelena, Lesh, Kathryn and Strumila, Michelle
(2022)
Normalizers of chains of discrete p-toral subgroups in compact Lie groups.
Topology and its Applications, , [108101].
(doi:10.1016/j.topol.2022.108101).
Abstract
In this paper we study the normalizer decomposition of a compact Lie group G using the information of the fusion system F of G on a maximal discrete p-toral subgroup. We prove that there is an injective map from the set of conjugacy classes of chains of F-centric, F-radical discrete p-toral subgroups to the set of conjugacy classes of chains of p-centric, p-stubborn continuous p-toral subgroups. The map is a bijection when π0(G) is a finite p-group. We also prove that the classifying space of the normalizer of a chain of discrete p-toral subgroups of G is mod p equivalent to the classifying space of the normalizer of the corresponding chain of p-toral subgroups.
Text
WIT_2019_Normalizers
- Accepted Manuscript
More information
Accepted/In Press date: 17 December 2021
e-pub ahead of print date: 7 April 2022
Published date: 1 July 2022
Keywords:
Classifying spaces, Compact Lie groups, Fusion, p-completion
Identifiers
Local EPrints ID: 454112
URI: http://eprints.soton.ac.uk/id/eprint/454112
ISSN: 0166-8641
PURE UUID: 21cfbcd0-7df9-4377-9731-7b0bfb5e88e8
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Date deposited: 31 Jan 2022 17:45
Last modified: 18 Mar 2024 05:28
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Contributors
Author:
Eva Belmont
Author:
Natàlia Castellana
Author:
Kathryn Lesh
Author:
Michelle Strumila
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