Equivariant cohomology, Koszul duality, and the localization theorem

Inventiones Mathematicae

Volumn 131, Issue 1, 1998, Pages 25-83

  Goresky, Mark ^a   Kottwitz, Robert ^b   Macpherson, Robert ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032345036     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050197     Document Type: Article

References (69)

1. C. Allday V. Puppe Cohomological Methods in Transformation Groups, Cambridge University Press, Cambridge (1993)
2. C. Allday, V. Puppe: On the localization theorem at the cochain level, Algebraic Topology, Göttingen 1984, Springer Lecture Notes in Mathematics Vol. 1172, Springer Verlag Berlin, Heidelberg, New York (1985)
3. M.F. Atiyah: Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14, 1-15 (1982)
4. M.F. Atiyah, R. Bott: The moment map and equivariant cohomology. Topology 23, 1-28 (1984)
5. M.F. Atiyah, G. Segal: Equivariant K-Theory, lecture notes, University of Warwick (1965)
6. M.F. Atiyah, G. Segal: Index of elliptic operators II Ann. Math. 87, 531-545 (1968)
7. M. Audin: The Topology of Torus Actions on Symplectic Manifolds, Progress in Mathematics vol. 93. Birkhauser Boston (1991)
8. n and problems of linear algebra, Funct. Anal. Appl. 12, 214-216 (1978)
9. A. Beilinson, J. Bernstein: A proof of the Jantzen conjectures, preliminary version
10. A. Beilison, J. Bernstein, P. Deligne: Faisceaux pervers, Astérisque 100, Soc. Math. de France (1982)
11. A. Beilinson, V. Ginzburg, W. Soergel: Koszul duality patterns in representation theory, to appear
12. N. Berline, M. Vergne: Zéros d'un champ de vecteurs et clases caractéristiques équivariantes, Duke Math J. 50, 19-83 (1985)
13. n and problems of linear algebra. Funct. Anal. Appl. 12, 212-214 (1978)
14. J. Bernstein, V. Lunts: Equivariant Sheaves and Functors. Lecture Notes in Math Vol. 1578, Springer Verlag N.Y. (1994)
15. A. Blanchard: Sur les variétés analytiques complexes. Ann. Sci. Ec. Norm. Sup. 73, 157-202 (1956)
16. A. Borel: Sur la cohomologie des espaces fibrés principaux et des espaces homogènes des groupes de Lie compacts, Ann. of Math. 57, 322-391 (1953)
17. A. Borel: Sur l'homologie et la cohomologie des groupes de Lie compacts connexes, Amer. J. Math 76, 273-342 (1954)
18. A. Borel: Seminar on Transformation Groups. Annals of Math Studies No. 46, Princeton University Press Princeton N.J. (1960)
19. A. Borel: Sheaf theoretic intersection cohomology, Seminar in Intersection Cohomology, Progress in Mathematics 50, Birkhauser Boston Boston MA (1984)
20. M. Brion: Piecewisc polynomial functions, convex polytopes, and enumerative geometry, Parameter Spaces, Proc. of Banach Center, 1994 Polish Acad. Sci. Warsaw
21. M. Brion, M. Vergue: An equivariant Riemann-Roch theorem for complete simplicial toric varieties, to appear
22. J.L. Brylinski: Equivariant intersection cohomology, Kazhdan-Lusztig Theory and Related Topics, Contemp. Math. vol 139, Amer. Math. Soc. Providence, R. I. pp 5-32 (1992)
23. S. Cappell, J. Shaneson: Euler-MacLaurin expansions for lattices above dimension one, C.R. Acad. Sci. Paris Série I 321, 885 890 (1995)
24. J. Carrell: The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties, Proc. Symp. Pure Math. 56 Amer. Math. Soc. Providence, R.I. 53-61 (1994)
25. H. Cartan: Notions d'algèbre differentielle; applications aux groupes de Lie et aux variétes ou opère un groupe de Lie, Colloque de Topologie (espaces fibrés), Bruxelles 1950 C.R.B.M. Paris (1951)
26. H. Cartan: La transgression dans un groupe de Lie et dans un espaces fibré principal, Colloque de Topologie (Espaces Fibrés), Bruxelles, 1950 C.R.B.M. Paris (1951)
27. T. Chang, T. Skjelbred: The topological Schur lemma and related results, Ann. Math. 100, 307-321 (1974)
28. P. Deligne: Théorème de Lefschetz et critères dedégénérescence de suites spectrales, Publ. Math. I.H.E.S. 35 Paris 107 -126 (1968)
29. P. Deligne: La conjecture de Weil II, Publ. Math. I.H.E.S. 44, 138-252 (1980)
30. P. Deligne: Poids dans la cohomologie des variétés algébriques, Proc. International Congresss of Mathematicians 1974 (R. D. James, rd.), Canadian Mathematical Congress (CMS) 79-86 (1974)
31. P. Deligne: Théorie de Hodge II, Publ. Math. I.H.E.S. 40, 5-58 (1971)
32. P. Deligne: Théorie de Hodge III, Publ. Math. I.H.E.S. 44, 5-77 (1975)
33. G. deRham: Differentiable Manifolds. Grund. Math. 266, Springer Verlag New York (1984)
34. T. tom: Dieck Transformation Groups. de Gruyeter Studied in Mathematics 8, Berlin, New York (1987)
35. J.J. Duistermaat, G. Heckman: On the variation in the cohomology in the symplectic form of the reduced phase space, Inv. Math. 69, 259-268 (1982)
36. E. B. Dynkin: Construction of primitive cycles in compact Lie groups, Doklady Akad. Nauk SSSR 91, 201-204 (1953)
37. S. Evens, I. Mirković: Fourier transform and the Iwahori-Matsumoto involution, preprint (1995)
38. V. Ginzburg: Equivariant cohomologies and Kähler's geometry (English translation), Funct. Anal. Appl. 21, 271-283 (1988)
39. M. Goresky, R. MacPherson: La dualité de Poincaré pour les espaces singuliers. C.R. Acad. Sci. Paris t.284, 1549-1551 (1977)
40. M. Goresky, R. MacPherson: Intersection homology theory. Topology 19, 135-162 (1980)
41. M. Goresky, R. MacPherson: Intersection homology II, Inv. Math. 71, 77-129 (1983)
42. M. Goresky, R. MacPherson: Local contribution to the Lefschetz fixed point formula, Inv. Math. 111, 1-33 (1993)
43. W. Greub, S. Halperin, S. Vanstone: Curvature, Connections, and Cohomology II, III. Academic Press New York, N.Y. (1976)
44. V. Guillemin, S. Sternberg: Convexity properties of the moment mapping. Inv. Math. 67, 491-513 (1982)
45. R. Hardt: Topological properties of subanalytic sets, Trans. Amer. Math. Soc. 211, 57-70 (1975)
46. H. Hironaka: Subanalytic sets, Number Theory, Algebraic Geometry and Commutative Algebra vol. in honor of A. Akizuki, Kinokunya Tokyo 453-493 (1973)
47. W.-Y. Hsiang: On some fundamental theorems in the cohomology theory of topological transformation groups, Taita (National Taiwan University) J. Math. 2, 66-87 (1970)
48. W.-Y. Hsiang: Some fundamental theorems in the cohomology theory of topological transformation groups, Bull. Amer. Math. Soc. 77, 1096-1098 (1971)
49. W.-Y. Hsiang: Cohomology Theory of Topological Transformation Groups. Erg. Math. 85, Springer Verlag Berlin, Heidelberg, New York 1975
50. D. Husemoller: Cyclic cohomology. Tata Institute Bombay, India
51. L. Illusie: Complexe cotangent et deformations II, Lecture Notes in Mathematics 283 1972 Springer Verlag New York, N.Y.
52. B. Iverson: Cohomology of Sheaves, Universitext, Springer Verlag 1986, New York, N.Y.
53. R. Joshua: Vanishing of odd-dimensional intersection homology, Math. Zeit. 195, 239-253 (1987)
54. R. Joshua: The intersection cohomology and the derived category of algebraic stacks, Algebraic K-theory and algebraic topology NATO ASI Ser. C 407 Kluwer 91-145 (1993)
55. M. Kashiwara, P. Schapira: Sheaves on Manifolds. Grundlehren vol. 292, Springer Verlag New York, N.Y. (1990)
56. C. Kassel: Cyclic homology, comodules, and mixed complexes, J. Algebra 107, 195-216 (1987)
57. C. Kassel: Quantum Groups. Graduate Texts in Mathematics vol. 155, Springer Verlag New York (1995)
58. F. Kirwan: Intersection homology and torus actions, J. Amer. Math. Soc. 1, 385-400 (1988)
59. F. Kirwan: Cohomology of Quotients in Symplectic and Algebraic Geometry. Mathematical Notes 31, Princeton University Press Princeton, N.J. (1984)
60. J.L. Koszul: Sur un type d'algebres differentielles en rapport avec la transgression, Colloque de Topologie (Espaces Fibrés), Bruxelles, 1950 C.R.B.M. Paris (1951)
61. P. Littleman, C. Procesi: Equivariant cohomology of wonderful compactifications, Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory, Progress in Mathematics 92, Birkhauser Boston Boston MA (1989)
62. L. Pontrjagin: Homologies in compact Lie groups, Mat. Sbornik 48, 389-422 (1939)
63. D.G. Quillen: The spectrum of an equivariant cohomology ring I, II, Ann. Math 94, 549-572, 573-602 (1971)
64. H. Samelson: Beiträge zur Topologie de Gruppen-Mannigfaltigkeiten, Ann. Math. 42, 1091-1137 (1941)
65. H. Samelson: Math Reviews p. 398 (1954)
66. G. Segal: Equivariant K-theory. Publ. Math. I.H.E.S. 34, 129-151 (1968)
67. J.-L. Verdier: Categories derivées, état 0, Cohomologie Étale, S.G.A. 41/2, Lecture Notes in Mathematics vol 569, Springer Verlag New York, N.Y. 262-311 (1977)
68. J.-L. Verdier: Dualité dans la cohomologie des espaces localements compacts, Sem. Bourbaki 300, (1965)
69. C. Weibel: An Introduction to Homological Algebra. Cambridge University Press, Cambridge (1994)