Comptes Rendus
Théorie des groupes
Note sur les formules de saut de Guillemin–Kalkman
[A Note on the formulas of Guillemin–Kalkman.]
Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 467-472.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.07.020
Paul-Émile Paradan 1

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

[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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