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Classifying spaces for commutativity of low-dimensional Lie groups

Part of: Lie groups Fiber spaces and bundles

Published online by Cambridge University Press:  12 July 2019

OMAR ANTOLÍN–CAMARENA ,
SIMON PHILIPP GRITSCHACHER  and
BERNARDO VILLARREAL
OMAR ANTOLÍN–CAMARENA
Affiliation:
Instituto de Matemáticas, UNAM, Mexico City. e-mail: omar@matem.unam.mx
SIMON PHILIPP GRITSCHACHER
Affiliation:
Centre for Symmetry and Deformation, University of Copenhagen. e-mail: gritschacher@math.ku.dk
BERNARDO VILLARREAL
Affiliation:
Instituto de Matemáticas, UNAM, Mexico City. e-mail: villarreal@matem.unam.mx
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Abstract

For each of the groups G = O(2), SU(2), U(2), we compute the integral and $\mathbb{F}_2$-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.

MSC classification

Primary: 55R40: Homology of classifying spaces, characteristic classes 22E99: None of the above, but in this section
Secondary: 55R20: Spectral sequences and homology of fiber spaces
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 169 , Issue 3 , November 2020 , pp. 433 - 478
Copyright
© Cambridge Philosophical Society 2019

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Footnotes

†

This author gratefully acknowledges financial support from the London Mathematical Society through a Postdoctoral Mobility Grant (PMG 16-17 22), and would like to thank the Pacific Institute for the Mathematical Sciences at the University of British Columbia for their hospitality. The author is supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92).

References

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