1. CMB 2013 (vol 57 pp. 225)
||Small Flag Complexes with Torsion|
We classify flag complexes on at most $12$ vertices with torsion in
the first homology group. The result is moderately computer-aided.
As a consequence we confirm a folklore conjecture that the smallest
poset whose order complex is homotopy equivalent to the real
projective plane (and also the smallest poset with torsion in the
first homology group) has exactly $13$ elements.
Keywords:clique complex, order complex, homology, torsion, minimal model
Categories:55U10, 06A11, 55P40, 55-04, 05-04
2. CMB 2011 (vol 55 pp. 632)
||Characterizations of Model Manifolds by Means of Certain Differential Systems|
We prove metric rigidity for complete manifolds supporting solutions of
certain second order differential systems, thus extending classical works on a
characterization of space-forms. Along the way, we also discover
new characterizations of space-forms. We next generalize results concerning metric
rigidity via equations involving vector fields.
Keywords:metric rigidity, model manifolds, Obata's type theorems
3. CMB 2011 (vol 55 pp. 487)
4. CMB 2008 (vol 51 pp. 146)
||Stepping-Stone Model with Circular Brownian Migration |
In this paper we consider the stepping-stone model on a circle with
circular Brownian migration. We first point out a connection between
Arratia flow on the circle and the marginal distribution of this
model. We then give a new representation for the stepping-stone
model using Arratia flow and circular coalescing Brownian motion.
Such a representation enables us to carry out some explicit
computations. In particular, we find the distribution for the first
time when there is only one type
left across the circle.
Keywords:stepping-stone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law
5. CMB 2001 (vol 44 pp. 459)
||LS-catÃ©gorie algÃ©brique et attachement de cellules |
Nous montrons que la A-cat\'egorie d'un espace simplement connexe de
type fini est inf\'erieure ou \'egale \`a $n$ si et seulement si son
mod\`ele d'Adams-Hilton 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 A-category of a simply connected space of finite type
is less than or equal to $n$ if and only if its Adams-Hilton 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:LS-category, strong category, Adams-Hilton models, cell attachments