Classifying spaces for commutativity of low-dimensional Lie groups

Omar Antolín-Camarena; Simon Philipp Gritschacher; Bernardo Villarreal

doi:10.1017/S0305004119000240

Classifying spaces for commutativity of low-dimensional Lie groups

Omar Antolín-Camarena^*
, Simon Philipp Gritschacher
, Bernardo Villarreal

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

For each of the groups G = O(2), SU(2), U(2), we compute the integral and-cohomology rings of B_comG (the classifying space for commutativity of G), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy type of E_comG (the homotopy fiber of the inclusion B_comG → BG), and some low-dimensional homotopy groups of B_comG.

Original language	English
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	169
Issue number	3
Pages (from-to)	433-478
ISSN	0305-0041
DOIs	https://doi.org/10.1017/S0305004119000240
Publication status	Published - 2020

Keywords

2010 Mathematics Subject Classification:
22E99
Primary: 55R40
Secondary: 55R20

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10.1017/S0305004119000240

Classifying spaces for commutativity of low-dimensional Lie groupsAccepted author manuscript, 533 KBLicence: Other

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Cite this

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title = "Classifying spaces for commutativity of low-dimensional Lie groups",

abstract = "For each of the groups G = O(2), SU(2), U(2), we compute the integral and-cohomology rings of BcomG (the classifying space for commutativity of G), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy type of EcomG (the homotopy fiber of the inclusion BcomG → BG), and some low-dimensional homotopy groups of BcomG.",

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AU - Gritschacher, Simon Philipp

AU - Villarreal, Bernardo

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N2 - For each of the groups G = O(2), SU(2), U(2), we compute the integral and-cohomology rings of BcomG (the classifying space for commutativity of G), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy type of EcomG (the homotopy fiber of the inclusion BcomG → BG), and some low-dimensional homotopy groups of BcomG.

AB - For each of the groups G = O(2), SU(2), U(2), we compute the integral and-cohomology rings of BcomG (the classifying space for commutativity of G), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy type of EcomG (the homotopy fiber of the inclusion BcomG → BG), and some low-dimensional homotopy groups of BcomG.

KW - 2010 Mathematics Subject Classification:

KW - 22E99

KW - Primary: 55R40

KW - Secondary: 55R20

U2 - 10.1017/S0305004119000240

DO - 10.1017/S0305004119000240

M3 - Journal article

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SP - 433

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