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Segre class and equivariant multiplicity. (Classe de Segre et multiplicité équivariantes.) (French) Zbl 0798.55006

Summary: Let \(G\) be a compact connected Lie group and let \({\mathcal E}\) denote a \(G\)- equivariant bundle. For every \(G\)-equivariant cone bundle \({\mathcal C}\) in \({\mathcal E}\) we define the \(G\)-equivariant Segre class of \({\mathcal C}\). We establish a multiplicative formula for \(G\)-invariant Segre class analogous to a conjectured equality of W. Borho, J.-L. Brylinski, W. Fulton and R. MacPherson.

MSC:

55N91 Equivariant homology and cohomology in algebraic topology
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[1] ATIYAH (M.F.) and BOTT (R.) . - The moment map and equivariant cohomology , Topology, t. 23, 1984 , p. 1-28. MR 85e:58041 | Zbl 0521.58025 · Zbl 0521.58025
[2] BORHO (W.) , BRYLINSKI (J.-L.) and MAC PHERS0N (R.) . - Nilpotent Orbits, Primitive Ideals and Characteristic Classes , Progress in Mathematics, 78, Birkhäuser, 1989 . MR 91d:17012 | Zbl 0697.17006 · Zbl 0697.17006
[3] BERLINE (N.) , GETZLER (E.) and VERGNE (M.) . - Heat kernels and the Dirac operator . - A paraître.
[4] BOTT (R.) and TU (L.W.) . - Differential Forms in Algebraic Topology . - Springer-Verlag, 1982 . MR 83i:57016 | Zbl 0496.55001 · Zbl 0496.55001
[5] CARTAN (H.) . - La transgression dans un groupe de Lie et dans un espace fibré principal , Coll. Topologie CBRM, 1950 , p. 57-71. MR 13,107f | Zbl 0045.30701 · Zbl 0045.30701
[6] CORNALBA (M.) and GRIFFITHS (P.) . - Analytic Cycles and Vector Bundles on Non-Compact Algebraic Varieties , Invent. Math., t. 28, 1975 , p. 1-106. MR 51 #3505 | Zbl 0293.32026 · Zbl 0293.32026
[7] DOUBROVINE (B.) , NOVIKOV (S.) and FOMENKO (A.) . - Géométrie contemporaine III . - Mir, 1987 .
[8] FULTON (W.) . - Intersection theory . - Springer-Verlag, 1984 . MR 85k:14004 | Zbl 0541.14005 · Zbl 0541.14005
[9] GRIFFITHS (P.) and HARRIS (J.) . - Principles of Algebraic Geometry . - John Wiley and Sons, 1978 . MR 80b:14001 | Zbl 0408.14001 · Zbl 0408.14001
[10] JOSEPH (A.) . - On the variety of a highest weight module , J. Algebra, t. 88, 1984 , p. 238-278. MR 85j:17014 | Zbl 0539.17006 · Zbl 0539.17006
[11] KING (J.R.) . - The currents defined by analytic varieties , Acta Math., t. 127, 1971 , p. 185-220. MR 52 #14359 | Zbl 0224.32008 · Zbl 0224.32008
[12] MATHAI (V.) and QUILLEN (D.) . - Superconnections, Thom classes, and equivariant differential forms , Topology, t. 25, 1986 , p. 85-110. MR 87k:58006 | Zbl 0592.55015 · Zbl 0592.55015
[13] ROSSMANN (W.) . - Equivariant multiplicities on complex varieties , Astérisque, t. 173/174, 1989 , p. 313-330. MR 91g:32042 | Zbl 0691.32004 · Zbl 0691.32004
[14] VERGNE (M.) . - Polynômes de Joseph et représentations de Springer , Ann. Sci. École Norm. Sup., t. 23, 1990 , p. 543-562. Numdam | MR 92c:17014 | Zbl 0718.22009 · Zbl 0718.22009
[15] VERONA (A.) . - Integration on Whitney prestratifications , Rev. Roumaine Math. Pures Appl., t. 17, 1972 , p. 1473-1480. MR 48 #6461 | Zbl 0248.57025 · Zbl 0248.57025
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