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2-Primary Exponent Bounds for Lie Groups of Low Rank

Published online by Cambridge University Press:  20 November 2018

Stephen D. Theriault
Stephen D. Theriault*
Affiliation:
Department of Mathematics University of Virginia Charlottesville, VA 22904 USA
*
Current address: Department of Mathematical Sciences University of Aberdeen Aberdeen AB24 3UE United Kingdom, email: s.theriault@maths.abdn.ac.uk
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Abstract

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Exponent information is proven about the Lie groups $SU(3),\,SU(4),\,Sp(2)$, and ${{G}_{2}}$ by showing some power of the $H$-space squaring map (on a suitably looped connected-cover) is null homotopic. The upper bounds obtained are $8,\,32,\,64$, and ${{2}^{8}}$ respectively. This null homotopy is best possible for $SU(3)$ given the number of loops, off by at most one power of 2 for $SU(4)$ and $Sp(2)$, and off by at most two powers of 2 for ${{G}_{2}}$.

Keywords

55Q52Lie groupexponent
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 1 , 01 March 2004 , pp. 119 - 132
Copyright
Copyright © Canadian Mathematical Society 2004

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