1. CMB 2013 (vol 57 pp. 526)
 Heil, Wolfgang; Wang, Dongxu

On $3$manifolds with Torus or Klein Bottle Category Two
A subset $W$ of a closed manifold $M$ is $K$contractible, where $K$
is a torus or Kleinbottle, if the inclusion $W\rightarrow M$ factors
homotopically through a map to $K$. The image of $\pi_1 (W)$ (for any
base point) is a subgroup of $\pi_1 (M)$ that is isomorphic to a
subgroup of a quotient group of $\pi_1 (K)$. Subsets of $M$ with this
latter property are called $\mathcal{G}_K$contractible. We obtain a
list of the closed $3$manifolds that can be covered by two open
$\mathcal{G}_K$contractible subsets. This is applied to obtain a list
of the possible closed prime $3$manifolds that can be covered by two
open $K$contractible subsets.
Keywords:LusternikSchnirelmann category, coverings of $3$manifolds by open $K$contractible sets Categories:57N10, 55M30, 57M27, 57N16 

2. CMB 2001 (vol 44 pp. 459)
 Kahl, Thomas

LScatÃ©gorie algÃ©brique et attachement de cellules
Nous montrons que la Acat\'egorie d'un espace simplement connexe de
type fini est inf\'erieure ou \'egale \`a $n$ si et seulement si son
mod\`ele d'AdamsHilton est un r\'etracte homotopique d'une alg\`ebre
diff\'erentielle \`a $n$ \'etages. Nous en d\'eduisons que
l'invariant $\Acat$ augmente au plus de 1 lors de l'attachement
d'une cellule \`a un espace.
We show that the Acategory of a simply connected space of finite type
is less than or equal to $n$ if and only if its AdamsHilton model is
a homotopy retract of an $n$stage differential algebra. We deduce
from this that the invariant $\Acat$ increases by at most 1 when a
cell is attached to a space.
Keywords:LScategory, strong category, AdamsHilton models, cell attachments Categories:55M30, 18G55 
