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Classifying spaces for commutativity of low-dimensional Lie groups

Published online by Cambridge University Press:  12 July 2019

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

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 BcomGBG), and some low-dimensional homotopy groups of BcomG.

Type
Research Article
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).

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