Homologie de contact des variétés toröıdales

Homology and K-theory of the Bianchi groups

We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group homology and equivariant K-homology. By the Baum/Connes conjecture, which holds for the Bianchi groups, we obtain the K-theory of their reduced C-algebras i...

Décomposition de Hodge pour l’homologie stable des groupes d’automorphismes des groupes libres

We establish a decomposition of stable homology of automorphism groups of free groups with polynomial contravariant coefficients in term of functor homology. This allows several explicit computations, intersecting results obtained by independant methods by O. Randal-Williams. Classification MSC 2010 : 18A25, 18G15, 20E36, 20J06, 55P42 (18A40, 18E30, 18G40, 55P47). Mots clefs : groupes d’automor...

The q = −1 phenomenon for bounded (plane) partitions via homology concentration

Algebraic complexes whose “faces” are indexed by partitions and plane partitions are introduced, and their homology is proven to be concentrated in even dimensions with homology basis indexed by fixed points of an involution, thereby explaining topologically two quite important instances of Stembridge’s q = −1 phenomenon. A more general framework of invariant and coinvariant complexes with coef...

Geometric aspects of rings and representations theories

Lors de la quantification algébrique d'une algèbre de Pois-son, il est intéressant que certains groupes de (co)homologie suivent cette déformation de Poisson en Hochschild. Nous présenterons ce thème relative-ment au groupe des traces en donnant des exemples provenant de variétés quotients par l'action de groupes finis, typiquement pour les singularités de Klein, les actions doublées de groupes...

Cohomologie L des variétés QALE