1. CJM 2009 (vol 62 pp. 284)
 Grbić, Jelena; Theriault, Stephen

SelfMaps of Low Rank Lie Groups at Odd Primes
Let G be a simple, compact, simplyconnected Lie group localized at an odd prime~p. We study the group of homotopy classes of selfmaps $[G,G]$ when the rank of G is low and in certain cases describe the set of homotopy classes of multiplicative selfmaps $H[G,G]$. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given.
Keywords:Lie group, selfmap, Hmap Categories:55P45, 55Q05, 57T20 

2. CJM 2007 (vol 59 pp. 1154)
 Boardman, J. Michael; Wilson, W. Stephen

$k(n)$TorsionFree $H$Spaces and $P(n)$Cohomology
The $H$space that represents BrownPeterson cohomology
$\BP^k ()$ was split by the second author into indecomposable
factors, which all have torsionfree 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 BoardmanJohnsonWilson; this relies heavily on the
RavenelWilson 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 RavenelWilsonYagita, 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 $\Sigma\Omega\Sigma X$,
HiltonMilnor one for $\Omega (\Sigma X\vee\Sigma Y)$, and CohenWu 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
HiltonMilnor decompositions have analogues when the suspensions are
replaced by coassociative co$H$ spaces, and the CohenWu decomposition
has an analogue when the (double) suspension is replaced by a coassociative,
cocommutative co$H$ space.
Categories:55P35, 55P45 
