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Classifying spaces for commutativity of low-dimensional Lie groups

  • OMAR ANTOLíN–CAMARENA (a1), SIMON PHILIPP GRITSCHACHER (a2) and BERNARDO VILLARREAL (a3)

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.

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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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MSC classification

Classifying spaces for commutativity of low-dimensional Lie groups

  • OMAR ANTOLíN–CAMARENA (a1), SIMON PHILIPP GRITSCHACHER (a2) and BERNARDO VILLARREAL (a3)

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