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Search: MSC category 55P45 ( \$H\$-spaces and duals )

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1. CJM 2009 (vol 62 pp. 284)

Grbić, Jelena; Theriault, Stephen
 Self-Maps of Low Rank Lie Groups at Odd Primes Let G be a simple, compact, simply-connected Lie group localized at an odd prime~p. We study the group of homotopy classes of self-maps \$[G,G]\$ when the rank of G is low and in certain cases describe the set of homotopy classes of multiplicative self-maps \$H[G,G]\$. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given. Keywords:Lie group, self-map, H-mapCategories:55P45, 55Q05, 57T20

2. CJM 2007 (vol 59 pp. 1154)

Boardman, J. Michael; Wilson, W. Stephen
 \$k(n)\$-Torsion-Free \$H\$-Spaces and \$P(n)\$-Cohomology The \$H\$-space that represents Brown--Peterson cohomology \$\BP^k (-)\$ was split by the second author into indecomposable factors, which all have torsion-free homotopy and homology. Here, we do the same for the related spectrum \$P(n)\$, by constructing idempotent operations in \$P(n)\$-cohomology \$P(n)^k (\$--\$)\$ in the style of Boardman--Johnson--Wilson; this relies heavily on the Ravenel--Wilson determination of the relevant Hopf ring. The resulting \$(i- 1)\$-connected \$H\$-spaces \$Y_i\$ have free connective Morava \$\K\$-homology \$k(n)_* (Y_i)\$, and may be built from the spaces in the \$\Omega\$-spectrum for \$k(n)\$ using only \$v_n\$-torsion invariants. We also extend Quillen's theorem on complex cobordism to show that for any space \$X\$, the \linebeak\$P(n)_*\$-module \$P(n)^* (X)\$ is generated by elements of \$P(n)^i (X)\$ for \$i \ge 0\$. This result is essential for the work of Ravenel--Wilson--Yagita, which in many cases allows one to compute \$\BP\$-cohomology from Morava \$\K\$-theory. Categories:55N22, 55P45

3. CJM 2003 (vol 55 pp. 181)

Theriault, Stephen D.
 Homotopy Decompositions Involving the Loops of Coassociative Co-\$H\$ Spaces James gave an integral homotopy decomposition of \$\Sigma\Omega\Sigma X\$, Hilton-Milnor one for \$\Omega (\Sigma X\vee\Sigma Y)\$, and Cohen-Wu gave \$p\$-local decompositions of \$\Omega\Sigma X\$ if \$X\$ is a suspension. All are natural. Using idempotents and telescopes we show that the James and Hilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-\$H\$ spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-\$H\$ space. Categories:55P35, 55P45