Note sur les formules de saut de Guillemin–Kalkman

Paul-Émile Paradan

doi:10.1016/j.crma.2004.07.020

Théorie des groupes

Note sur les formules de saut de Guillemin–Kalkman
[A Note on the formulas of Guillemin–Kalkman.]

Presented by: Michèle Vergne

Paul-Émile Paradan ¹

¹ UMR 5582, institut Fourier, B.P. 74, 38402 Saint-Martin-d'Hères cedex, France

Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 467-472.

Abstract
Résumé

The purpose of this Note is to give a jump formula in equivariant cohomology implying the jump formulas of Guillemin–Kalkman.

Le but de cette Note est de donner une formule de saut en cohomologie équivariante qui entraîne les formules de saut de Guillemin–Kalkman (J. Reine Agnew. Math. 470 (1996) 123–142).

Received: 2004-06-28
Accepted: 2004-07-12
Published online: 2004-09-25

DOI: 10.1016/j.crma.2004.07.020

Author's affiliations:

Paul-Émile Paradan ¹

¹ UMR 5582, institut Fourier, B.P. 74, 38402 Saint-Martin-d'Hères cedex, France

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     title = {Note sur les formules de saut de {Guillemin{\textendash}Kalkman}},
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Paul-Émile Paradan. Note sur les formules de saut de Guillemin–Kalkman. Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 467-472. doi : 10.1016/j.crma.2004.07.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.020/

References
Cited by

[1] N. Berline; E. Getzler; M. Vergne Heat Kernels and Dirac Operators, Grundlehren Math. Wiss., vol. 298, Springer, Berlin, 1991

[2] V. Guillemin; J. Kalkman The Jeffrey–Kirwan localization theorem and residue operations in equivariant cohomology, J. Reine Angew. Math., Volume 470 (1996), pp. 123-142

[3] V. Guillemin; S. Sternberg Supersymmetry and Equivariant de Rham Theory, Springer-Verlag, Berlin, 1999 (With an appendix containing two reprints by Henri Cartan, Mathematics Past and Present)

[4] F. Kirwan Cohomology of Quotients in Symplectic and Algebraic Geometry, Princeton University Press, Princeton, 1984

[5] S. Kumar; M. Vergne Equivariant cohomology with generalized coefficients, Astérisque, Volume 215 (1993), pp. 109-204

[6] P.-E. Paradan Formules de localisation en cohomologie équivariante, Compositio Math., Volume 117 (1999), pp. 243-293

[7] P.-E. Paradan The moment map and equivariant cohomology with generalized coefficients, Topology, Volume 163 (2000), pp. 401-444

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