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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, exponentCategory:55Q52

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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