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Normalizers of chains of discrete p-toral subgroups in compact Lie groups

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
0166-8641
1-18
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
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, 1-18, [108101]. (doi:10.1016/j.topol.2022.108101).

Record type: Article

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.

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WIT_2019_Normalizers - Accepted Manuscript
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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
ORCID for Jelena Grbić: ORCID iD orcid.org/0000-0002-7164-540X

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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: Jelena Grbić ORCID iD
Author: Kathryn Lesh
Author: Michelle Strumila

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