论文信息 - On the localization theorem in equivariant cohomology

On the localization theorem in equivariant cohomology

We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie group. This applies in particular to smooth, projective spherical varieties.

M. Brion | M. Vergne

[1] M. Goresky,et al. Equivariant cohomology, Koszul duality, and the localization theorem , 1997 .

[2] Michel Brion,et al. Equivariant Chow groups for torus actions , 1997 .

[3] C. Woodward. The classification of transversal multiplicity-free group actions , 1996 .

[4] M. Audin. The Topology of Torus Actions on Symplectic Manifolds , 1991 .

[5] Santhosh K. P. Kumar,et al. The nil Hecke ring and cohomology of G/P for a Kac-Moody group G. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[6] A. Arabia. Cycles de Schubert et cohomologie équivariante de K/T , 1986 .

[7] Theodore Chang,et al. Topological Schur lemma and related results , 1973 .

[8] P. Iglesias. Les SO(3)-variétés symplectiques et leur classification en dimension 4 , 1991 .

[9] S. Sternberg,et al. Multiplicity-free spaces , 1984 .

[10] W. Hsiang,et al. Cohomology Theory of Topological Transformation Groups , 1975 .