Automorphic representations and Lefschetz numbers
Bar complexes and extensions of classical exponential functors
We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac Lane spaces.This article completes earlier results of the author, and provides an alternative approach to classical Ext-computations in the category of strict polynomial functors over fields. We also obtain significant Ext-computations for strict polynomial functors...
Bounded cohomology of lattices in higher rank Lie groups
We prove that the natural map from bounded to usual cohomology is injective if is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for : the stable commutator length vanishes and any –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating to the continuous bounded cohomology of the ambient group...
Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds
We estimate the characteristic rank of the canonical –plane bundle over the oriented Grassmann manifold . We then use it to compute uniform upper bounds for the –cup-length of for belonging to certain intervals.
Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space
DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated...
Categories equivalent to the category of rational H-spaces.
Category of -categories.
Characteristic zero loop space homology for certain two-cones
Given a principal ideal domain of characteristic zero, containing 1/2, and a two-cone of appropriate connectedness and dimension, we present a sufficient algebraic condition, in terms of Adams-Hilton models, for the Hopf algebra to be isomorphic with the universal enveloping algebra of some -free graded Lie algebra; as usual, stands for free part, for homology, and for the Moore loop space functor.
Classification of compact complex homogeneous spaces with invariant volumes.
Cobordisme d'immersions
Cochain operations defining Steenrod--products in the bar construction.
Cohomologie de et valeurs de fonctions zêta aux points entiers
Cohomologie des groupes discrets
Cohomologie T-équivariante de la variété de drapeaux d'un groupe de Kač-Moody
Cohomologies de certaines formes sphériques
Cohomology eigenvalues of equivariant mappings.
Cohomology mod3 of the classifying space of the Lie group E...
Cohomology of arithmetic subgroups of SL3 at infinity.
Cohomology of biquotients.
Cohomology of Congruence Subgroups of SL (n,Z).