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Spaces of commuting elements in SU(2)

Part of: Homotopy theory

Published online by Cambridge University Press:  19 January 2011

M. C. Crabb
M. C. Crabb
Affiliation:
Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, UK
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Abstract

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Based on the work of Adem and Cohen, this note describes an explicit stable decomposition of the space of commuting n-tuples in SU(2) as a wedge of indecomposable summands.

Keywords

equivariant stable homotopystable splittingfinite graph

MSC classification

Secondary: 55P42: Stable homotopy theory, spectra 55P91: Equivariant homotopy theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 1 , February 2011 , pp. 67 - 75
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Adem, A. and Cohen, F. R., Commuting elements and spaces of homomorphisms, Math. Annalen 338 (2007), 587–626.CrossRefGoogle Scholar
2.Adem, A. and Cohen, F. R., Commuting elements and spaces of homomorphisms: erratum, Math. Annalen 347 (2010), 245–248.CrossRefGoogle Scholar
3.Baird, T. J., Cohomology of the space of commuting n-tuples in a compact Lie group, Alg. Geom. Topol. 7 (2007), 737–754.CrossRefGoogle Scholar
4.Baird, T. J., Jeffrey, L. and Selick, P., The space of commuting n-tuples in SU(2), preprint (arXiv: 091.4953v3 [math.AT]).Google Scholar
5.Crabb, M. C., Hubbuck, J. R. and McCall, J. A. W., Stable summands of U(n), Proc. R. Soc. Edinb. A 127 (1997), 963–973.CrossRefGoogle Scholar
6.Miller, H., Stable splittings of Stiefel manifolds, Topology 24 (1985), 411–419.CrossRefGoogle Scholar