1. CJM Online first
 Cordova Bulens, Hector; Lambrechts, Pascal; Stanley, Don

Rational models of the complement of a subpolyhedron in a manifold with boundary
Let $W$ be a compact simply connected triangulated manifold with
boundary and $K\subset W$ be a subpolyhedron. We construct an
algebraic model of the rational homotopy type of $W\backslash K$ out of
a model of the map of pairs $(K,K \cap \partial W)\hookrightarrow
(W,\partial W)$ under some high codimension hypothesis.
We deduce the rational homotopy invariance of the configuration
space
of two points in a compact manifold with boundary under 2connectedness
hypotheses. Also, we exhibit
nice explicit models of these configuration spaces for a large
class
of compact manifolds.
Keywords:Lefschetz duality, Sullivan model, configuration space Categories:55P62, 55R80 

2. CJM 2012 (vol 65 pp. 82)
 Félix, Yves; Halperin, Steve; Thomas, JeanClaude

The Ranks of the Homotopy Groups of a Finite Dimensional Complex
Let $X$ be an
$n$dimensional, finite, simply connected CW complex and set
$\alpha_X =\limsup_i \frac{\log\mbox{ rank}\, \pi_i(X)}{i}$. When
$0\lt \alpha_X\lt \infty$, we give upper and lower bound for $
\sum_{i=k+2}^{k+n} \textrm{rank}\, \pi_i(X) $ for $k$ sufficiently
large. We show also for any $r$ that $\alpha_X$ can be estimated
from the integers rk$\,\pi_i(X)$, $i\leq nr$ with an error bound
depending explicitly on $r$.
Keywords:homotopy groups, graded Lie algebra, exponential growth, LS category Categories:55P35, 55P62, , , , 17B70 

3. CJM 2004 (vol 56 pp. 1290)
 Scull, Laura

Equivariant Formality for Actions of Torus Groups
This paper contains a comparison of several
definitions of equivariant formality for actions of torus groups. We
develop and prove some relations between the definitions. Focusing on
the case of the circle group, we use $S^1$equivariant minimal models
to give a number of examples of $S^1$spaces illustrating the
properties of the various definitions.
Keywords:Equivariant homotopy, circle action, minimal model,, rationalization, formality Categories:55P91, 55P62, 55R35, 55S45 

4. CJM 2002 (vol 54 pp. 608)
 Stanley, Donald

On the LusternikSchnirelmann Category of Maps
We give conditions which determine if $\cat$ of a map go up when
extending over a cofibre. We apply this to reprove a result of
Roitberg giving an example of a CW complex $Z$ such that $\cat(Z)=2$
but every skeleton of $Z$ is of category $1$. We also find conditions
when $\cat (f\times g) < \cat(f) + \cat(g)$. We apply our result to
show that under suitable conditions for rational maps $f$, $\mcat(f) <
\cat(f)$ is equivalent to $\cat(f) = \cat (f\times \id_{S^n})$. Many
examples with $\mcat(f) < \cat(f)$ satisfying our conditions are
constructed. We also answer a question of Iwase by constructing
$p$local spaces $X$ such that $\cat (X\times S^1) = \cat(X) = 2$. In
fact for our spaces and every $Y \not\simeq *$, $\cat (X\times Y) \leq
\cat(Y) +1 < \cat(Y) + \cat(X)$. We show that this same $X$ has the
property $\cat(X) = \cat (X\times X) = \cl (X\times X) = 2$.
Categories:55M30, 55P62 

5. CJM 1999 (vol 51 pp. 49)
 Ndombol, Bitjong; El haouari, M.

AlgÃ¨bres quasicommutatives et carrÃ©s de Steenrod
Soit $k$ un corps de caract\'eristique $p$ quelconque. Nous
d\'efinissons la cat\'egorie des $k$alg\`ebres de cocha\^{\i}nes
fortement quasicommutatives et nous donnons une condition
n\'ecessaire et suffisante pour que l'alg\`ebre de cohomologie \`a
coefficients dans $\mathbb{Z}_2$ d'un objet de cette cat\'egorie soit
un module instable sur l'alg\`ebre de Steenrod \`a coefficients dans
$\mathbb{Z}_2$.
A tout c.w.\ complexe simplement connexe de type fini $X$ on associe une
$k$alg\`ebre de cocha\^{\i}nes fortement quasicommutative; la
structure de module sur l'alg\`ebre de Steenrod d\'efinie sur
l'alg\`ebre de cohomologie de celleci co\"\i ncide avec celle de
$H^*(X; \mathbb{Z}_2)$.
We define the category of strongly quasicommutative cochain
$k$algebras, where $k$ is a field of any characteristic $p$. We give a
necessary and sufficient condition which enables the cohomology algebra
with $\mathbb{Z}_2$coefficients of an object in this category
to be an unstable module on the $\mathbb{Z}_2$Steenrod algebra.
To each simply connected c.w.\ complex of finite type $X$ is associated
a strongly quasicommutative model and the module structure over the
$\mathbb{Z}_2$Steenrod algebra defined on the cohomology of
this model is the usual structure on $H^*(X; \mathbb{Z}_2)$.
Keywords:algÃ¨bres de cocha\^{\i}nes (fortement) quasicommutatives, $T (V)$modÃ¨le, carrÃ©s de Steenrod, quasiisomorphisme Categories:55P62, 55S05 

6. CJM 1998 (vol 50 pp. 845)
 Scheerer, H.; Tanré, D.

LusternikSchnirelmann category and algebraic $R$local homotopy theory
In this paper, we define the notion of $R_{\ast}$$\LS$ category
associated to an increasing system of subrings of $\Q$ and we relate
it to the usual $\LS$category. We also relate it to the invariant
introduced by F\'elix and Lemaire in tame homotopy theory, in which
case we give a description in terms of Lie algebras and of cocommutative
coalgebras, extending results of LemaireSigrist and F\'elixHalperin.
Categories:55P50, 55P62 

7. CJM 1997 (vol 49 pp. 855)
 Smith, Samuel Bruce

Rational Classification of simple function space components for flag manifolds.
Let $M(X,Y)$ denote the space of all continous functions
between $X$ and $Y$ and $M_f(X,Y)$ the path component
corresponding to a given map $f: X\rightarrow Y.$ When $X$ and
$Y$ are classical flag manifolds, we prove the components of
$M(X,Y)$ corresponding to ``simple'' maps $f$ are classified
up to rational homotopy type by the dimension of the kernel of
$f$ in degree two
cohomology. In fact, these components are themselves all products
of flag manifolds and odd spheres.
Keywords:Rational homotopy theory, SullivanHaefliger model. Categories:55P62, 55P15, 58D99. 
