For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations. Bredon [1] introduced what is now called Bredon cohomology, with the purpose of developing obstruction theory in the context of ...

Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory operation connected with the non compactness of the gauge group. The respective roles of fields and observables are emphasized throughout. ENSLAPP-A-619/96 CERN-TH/9...

In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group Gal(C/R). Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour’s quaternionic K-theory, and the other one classifies and equivariant cohomology theory Z∗(−) which is a natural recip...

An equivariant bundle gerbe à la Meinrenken over a G-manifold M is known to be a special type of S-gerbe over the differentiable stack [M/G]. We prove that the natural morphism relating the Cartan and simplicial models of equivariant cohomology in degree 3 maps the Dixmier-Douady class of an equivariant bundle gerbe à la Meinrenken to the Behrend-Xu-Dixmier-Douady class of the corresponding S-g...

Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X , generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reduc...

In the previous paper [17], the author defined equivariant Floer cohomology for a complete intersection in a toric variety and showed that it is isomorphic to the small quantum D-module after a mirror transformation when the first Chern class c1(M) of the tangent bundle is nef. In this paper, even when c1(M) is not nef, we show that the equivariant Floer cohomology reconstructs the big quantum ...

In this paper we present a cohomological description of the equivariant Brauer group relative to a Galois finite extension of fields endowed with the action of a group of operators. This description is a natural generalization of the classic Brauer–Hasse–Noether’s theorem, and it is established by means of a three-term exact sequence linking the relative equivariant Brauer group, the 2nd cohomo...

In this paper, we compute the $BP$ -cohomology of complex projective Stiefel manifolds. The method involves homotopy fixed point spectral sequence, and works for oriented cohomology theories. We also use these calculations -operations to prove new results about equivariant maps between

We give two generalizations of the Atiyah-Bott-Berline-Vergne lo-calization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calculating the Gysin homomorphism in ordinary co-homology of an equivariant map. A...

The present paper will form part of the author’s PhD thesis, which will concern in part the practical computation of the motivic cohomology and the equivariant motivic cohomology of homogeneous varieties, such as Stiefel manifolds, Grassmanians, and spaces of matrices with prescribed rank conditions. Nothing proved here is particularly surprising, but it seems to the author that the spectral se...