$2$-Primary Exponent Bounds for Lie Groups of Low Rank
Printed: Mar 2004
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 $G_2$.
Lie group, exponent
55Q52 - Homotopy groups of special spaces