Cyclic homology and equivariant homology.
Cyclic homology and equivariant theories
In this article, we present two possible extensions of the classical theory of equivariant cohomology. The first, due to P. Baum, R. MacPherson and the author, is called the “delocalized theory". We attempt to present it in very concrete form for a circle action on a smooth manifold. The second is the cyclic homology of the crossed- product algebra of the algebra of smooth functions on a manifold, by the convolution algebra of smooth functions on a Lie group, when such Lie group act on the manifold....
Décomposition de Hodge basique pour un feuilletage riemannien
Soit un feuilletage de codimension sur une variété compacte . On montre que le complexe des formes basiques admet une décomposition de Hodge. Il en résulte que la cohomologie basique de est de dimension finie et vérifie la dualité de Poincaré si et seulemnt si .
Decomposition numbers for perverse sheaves
The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial nilpotent orbit in a simple Lie algebra.This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive...
Depth and equivariant cohomology.
Der Cohomologiering von komplexen Quadriken.
Der Conner-Floyd-Isomorphismus für Abelsche Gruppen.
Der Einfluss von K*(-) auf U* (-).
Der freie Schleifenraum für Räume mit fast freier rationaler Kohomologie-Algebra.
Der Pontryagin-Ring von Quotienten eines Torus.
Describing toric varieties and their equivariant cohomology
Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even...
Detecting Stable Homotopy Classes by Primary BP Cohomology Operations.
Die 1/2-Lokalisierung des Spektrums MSO.
Die Bestimmung der unitären K-Theorie von S0(n) mit Hilfe der Atiyah-Hirzebruch-Spektralreihe.
Die homotopiekategorie der Boardman-Spektren ist zur Homotopiekategorie der Kan-Spektren Äquivalent
Die Signatur von Flächenbündeln.
Direct Images of Sheaves of Differentials and the Atiyah Class.
Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere.
Dualité dans la cohomologie des espaces localement compacts
Effective homology for homotopy colimit and cofibrant replacement
We extend the notion of simplicial set with effective homology presented in [22] to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets such that each simplicial set has effective homology, we present an algorithm computing the homotopy colimit as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement of as a diagram with effective homology. This is applied to computing of equivariant cohomology operations....