1. CMB 2004 (vol 47 pp. 119)
||$2$-Primary Exponent Bounds for Lie Groups of Low Rank |
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:Lie group, exponent
2. CMB 2000 (vol 43 pp. 226)
||James-Hopf Invariants, Anick's Spaces, and the Double Loops on Odd Primary Moore Spaces |
Using spaces introduced by Anick, we construct a decomposition into
indecomposable factors of the double loop spaces of odd primary Moore
spaces when the powers of the primes are greater than the first power.
If $n$ is greater than $1$, this implies that the odd primary part
of all the homotopy groups of the $2n+1$ dimensional sphere lifts
to a $\mod p^r$ Moore space.