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Search: MSC category 55Q52 ( Homotopy groups of special spaces )

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1. CMB 2004 (vol 47 pp. 119)

Theriault, Stephen D.
$2$-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)

Neisendorfer, Joseph
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.

Categories:55Q52, 55P35

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