Localizations of unstable A-modules and equivariant mod p cohomology.
On equivariant maps between Stiefel manifolds.
On Hochschild and cyclic homology of certain homogeneous spaces
On localization in holomorphic equivariant cohomology
We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.
On nonsingular matrices and Bott periodicity.
On -equivariant homology.
On the Groups JOGX. I.
Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups
Let G be a compact Lie group. We present a criterion for the orbit spaces of two G-spaces to be homotopy equivalent and use it to obtain a quick proof of Webb’s conjecture for compact Lie groups. We establish two Minami type formulae which present the p-localised spectrum as an alternating sum of p-localised spectra for subgroups H of G. The subgroups H are calculated from the collections of the non-trivial elementary abelian p-subgroups of G and the non-trivial p-radical subgroups of G. We...
Parity sheaves, moment graphs and the -smooth locus of Schubert varieties
We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the -smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.
Periodic equivariant Real k-theories have rational Tate theory.
Reflexive and dihedral (co)homology of a pre-additive category.
Sheaves on Fixed Point Sets and Equivariant Cohomology.
Smith theory and quasi-periodicity in Bredon cohomology
Some spectral sequences in Bredon cohomology
Sommes de Dedekind elliptiques et formes de Jacobi
À partir des formes de Jacobi , on construit une somme de Dedekind elliptique. On obtient ainsi un analogue elliptique aux sommes multiples de Dedekind construites à partir des fonctions cotangentes, étudiées par D. Zagier. En outre, on établit une loi de réciprocité satisfaite par ces nouvelles sommes. Par une procédure de limite, on peut retrouver la loi de réciprocité remplie par les sommes multiples de Dedekind classiques. D’autre part, en les spécialisant en des paramètres de points de 2- division,...
Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.
It is not known whether or not the stable rational cohomology groups H*(Aut(F∞);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields...
Sur la complétion de la -théorie équivariante
Sur les orbites d’un sous-groupe sphérique dans la variété des drapeaux
Soient un groupe algébrique complexe réductif et connexe, un sous-groupe de Borel de et un sous-groupe sphérique de . Soit un plongement -équivariant de . Nous savons que n’a qu’un nombre fini d’orbites dans ; nous montrons qu’il n’en a qu’un nombre fini dans . Soit l’adhérence dans d’une orbite de dans et l’adhérence d’une orbite de dans . Si est toroïdal, nous montrons que l’intersection est propre dans et la décrivons ensemblistement. Si de plus est lisse,...
Tensor products of categories of equivariant perverse sheaves
The Jeffrey-Kirwan localization theorem and residue operations in equivariant cohomology.