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An example of an asymptotically Chow unstable manifold with constant scalar curvature

Hajime Ono, Yuji Sano, Naoto Yotsutani (2012)

Annales de l’institut Fourier

Donaldson proved that if a polarized manifold ( V , L ) has constant scalar curvature Kähler metrics in c 1 ( L ) and its automorphism group Aut ( V , L ) is discrete, ( V , L ) is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where Aut ( V , L ) is not discrete.

Cohomologie et K-théorie équivariantes des variétés de Bott-Samelson et des variétés de drapeaux

Matthieu Willems (2004)

Bulletin de la Société Mathématique de France

L’objet de cet article est de calculer la cohomologie et la K-théorie équivariantes des variétés de Bott-Samelson (théorèmes 3.3 et 4.3) et d’en déduire des résultats sur les variétés de drapeaux des groupes de Kac-Moody. Dans la section 3, on retrouve la formule de restriction aux points fixes de la base { ξ ^ w } w W de H T * ( G / B ) (théorème 3.9) prouvée par Sara Billey dans [4]. Dans la section 4, on donne l’expression explicite de la restriction aux points fixes de la base { ψ ^ w } w W de K T ( G / B ) définie par Kostant et Kumar dans...

Componentwise injective models of functors to DGAs

Marek Golasiński (1997)

Colloquium Mathematicae

The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.

Conjugation spaces.

Hausmann, Jean-Claude, Holm, Tara, Puppe, Volker (2005)

Algebraic & Geometric Topology

Cyclic homology and equivariant theories

Jean-Luc Brylinski (1987)

Annales de l'institut Fourier

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....

Describing toric varieties and their equivariant cohomology

Matthias Franz (2010)

Colloquium Mathematicae

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...

Effective homology for homotopy colimit and cofibrant replacement

Marek Filakovský (2014)

Archivum Mathematicum

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 X : sSet such that each simplicial set X ( i ) has effective homology, we present an algorithm computing the homotopy colimit hocolim X as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement X cof of X as a diagram with effective homology. This is applied to computing of equivariant cohomology operations....

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