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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Continuous cohomology of groups and classifying spaces


Author: James D. Stasheff
Journal: Bull. Amer. Math. Soc. 84 (1978), 513-530
MSC (1970): Primary 55F35, 55F40, 55B35, 55H99; Secondary 17B65, 18H25, 18H10, 57F15
DOI: https://doi.org/10.1090/S0002-9904-1978-14488-7
MathSciNet review: 0494071
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  • 1. D. Baker, On a class of foliations and the evaluations of their characteristic classes, Thesis, SUNY, Stony Brook, 1976. MR 438351
  • 2. D. Baker, Differential characters and Borel cohomology, Topology 16 (1977), 441-449. MR 646086
  • 3. I. N. Bernšteĭn and B. I. Rosenfel'd, Homogeneous spaces of infinite-dimensional Lie algebras and characteristic classes of foliations, Russian Math Surveys 28 (1973), 107-142. MR 415633
  • 4. A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology 2 (1963), 111-122. MR 146301
  • 5. A. Borel, Seminar notes IAS 1976-1977.
  • 6. R. Bott (with L. Conlon), Lectures on characteristic classes, Lecture Notes in Math., vol. 279, Springer-Verlag, Berlin and New York, 1972, pp. 1-94. MR 362335
  • 7. R. Bott, On the Chern-Weil homomorphism and the continuous cohomology of Lie groups, Advances in Math. 11 (1973), 289-303. MR 345115
  • 8. R. Bott, Some remarks on continuous cohomology, Proc. Internat. Congress on Manifolds (Tokyo, 1973), Univ. of Tokyo Press, Tokyo, 1975, pp. 161-170. MR 368027
  • 9. R. Bott, H. Shulman and J. Stasheff, On the de Rham theory of classifying spaces, Advances in Math. 20 (1976), 43-56. MR 402769
  • 10. L. G. Brown, Extensions of topological groups, Pacific J. Math. 39 (1971), 71-78. MR 307264
  • 11. H. Cartan, Notions d'algèbre différentielle, Colloq. de Topologie Bruxelles, 1950, pp. 15-27. MR 42426
  • 12. J-L. Cathelineau, Un objet simplicial associé à un recouvrement d'un groupe topologique, Université de Poitiers (preprint).
  • 13. W. Casselman and D. Wigner, Continuous cohomology and a conjecture of Serre's, Invent. Math. 25 (1974), 199-211. MR 352333
  • 14. J. Cheeger and J. Simons, Jr., Differential characters and geometric invariants, SUNY, Stony Brook, (preprint). SUNY, Stony Brook, cf. C. Roger, Caractères différentiels, Lecture Notes in Math., vol. 484, Springer-Verlag, Berlin and New York, 1975, pp. 162-178. MR 827262
  • 15. C. Chevalley and S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124. MR 24908
  • 16. A. Dold and R. Lashof, Principal quasifibrations and fibre homotopy equivalence of bundles, Illinois J. Math. 3 (1959), 285-305. MR 101521
  • 17. J. L. Dupont, Simplicial de Rham cohomology and characteristic classes of flat bundles, Topology 15 (1976), 233-246. MR 413122
  • 18. D. B. Fuks, Characteristic classes of foliations, Russian Math. Surveys 28 (1973), 1-16. MR 415635
  • 19. I. M. Gel'fand and D. B. Fuks, Cohomologies of the Lie algebra of tangent vector fields of a smooth manifold, Functional Anal. Appl. 3 (1969), 194-210. MR 256411
  • 20. I. M. Gel'fand and D. B. Fuks, The cohomology of the Lie algebra of formal vector fields, Izvestia 34 (1970), 322-337. MR 266195
  • 21. C. Godbillon, Cohomologie d'algèbres de Lie de champs de vecteurs formels, Séminaire Bourbaki 421 (1972/73).
  • 22. C. Godbillon and J. Vey, Un invariant des feuilletages de codimension un, C. R. Acad. Sci. Paris 273 (1971), 92. MR 283816
  • 23. W. Greub, S. Halperin and R. Van Stone, Connections, curvature and cohomology. III, Academic Press, New York, 1976, p. 254. MR 400275
  • 24. A. Haefliger, Sur les classes caracteristiques des feuilletages, Séminaire Bourbaki 412 (1972/73). MR 420655
  • 25. A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), 183-194. MR 263104
  • 26. J. Heitsch, Deformations of secondary characteristic classes, Topology 12 (1973), 381-388. MR 321106
  • 27. J. Heitsch, Independent variation of secondary classes (manuscript).
  • 28. A. Heller, Principal bundles and group extensions with applications to Hopf algebras, J. Pure Appl. Algebra 3 (1973), 219-250. MR 327871
  • 29. G. P. Hochschild and G. D. Mostow, Cohomology of Lie groups, Illinois J. Math. 6 (1962), 367-401. MR 147577
  • 30. S-T Hu, Cohomology rings of compact connected groups and their homogeneous spaces, Ann. of Math (2) 55 (1952), 391-419. MR 47054
  • 31. S-T Hu, Cohomology theory in topological groups, Michigan Math. J. 1 (1952), 11-59. MR 51244
  • 32. F. Kamber and Ph. Tondeur, Characteristic invariants of foliated bundles, Manuscripta Math. 11 (1974), 51-89. MR 334237
  • 33. F. Kamber and Ph. Tondeur, On the linear independence of certain cohomology classes of BГ (preprint).
  • 34. M. Lazard, Groupes analytiques p-adiques, Publ. Math. IHES 26 (1975).
  • 35. S. Lie, Om en classe geometriske Transformationen, Ges. der Wiss. zu Christiania, 1870.
  • 36. S. Lie, Theorie der Transformations-gruppen, Teubner, Leipzig, 1890.
  • 37. G. Mackey, Les ensembles Boreliens et les extension des groupes, J. Math. Pures Appl. 36 (1957), 171-178. MR 89998
  • 38. S. Mac Lane, Homology, Die Grundlehren der Math. Wissenschaften, vol. 114, Springer-Verlag, Berlin and New York, 1963. MR 349792
  • 39. S. Mac Lane, Retiring Presidential Address, Bull. Amer. Math. Soc. 82 (1976), 1-40.
  • 40. S. Mac Lane, The work of Samuel Eilenberg in Topology, Algebra, topology, and category theory: a collection of papers in honor of Samuel Eilenberg, Academic Press, New York, 1976, p. 137. MR 414284
  • 41. R. J. Milgram, The bar construction and abelian H-spaces, Illinois J. Math 11 (1967), 242-250. MR 208595
  • 42. J. W. Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430-436. MR 77932
  • 43. C. C. Moore, Extensions and low dimensional cohomology theory of locally compact groups. I, II, Trans. Amer. Math. Soc. 113 (1964), 40-86; III, IV, Trans. Amer. Math. Soc. 221 (1976), 1-58. MR 171880
  • 44. C. C. Moore, Group extensions and group cohomology, Battelle Seattle Summer Rencontre, Lecture Notes in Math., Springer-Verlag, Berlin and New York, 1970, pp. 17-36. MR 279232
  • 45. J. C. Moore, Algèbre homologique et homologie des espaces classifiants, Séminaire H. Cartan (1959/60).
  • 46. S. Morita, A remark on the continuous variation of secondary characteristic classes for foliations (preprint). MR 442952
  • 47. P. S. Mostert, Local cross section in locally compact groups, Proc. Amer. Math. Soc. 4 (1953), 645-649. MR 56614
  • 48. G. D. Mostow, Cohomology of topological groups and solvmanifolds, Ann. of Math. (2) 73 (1961), 20-48. MR 125179
  • 49. M. A. Mostow, Continuous cohomology of spaces with two topologies, Mem. Amer. Math. Soc. No. 175 (1976). MR 413132
  • 50. M. Mostow and J. Perchik, Notes on Gel'fand-Fuks cohomology and characteristic classes (Lectures by Raoul Bott), New Mexico State Univ., 1973.
  • 51. O. H. Rasmussen, Non-vanishing and continuous variation of exotic characteristic classes for foliations, Thesis, Princeton Univ., 1974.
  • 52. G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-312. MR 353298
  • 53. G. Segal, Cohomology of topological groups, Symposia Mathematica IV (1970), 377-387. MR 280572
  • 54. J-P. Serre, Cohomologie Galoisienne, Lecture Notes in Math., vol. 5, Springer-Verlag, Berlin and New York, 1973. MR 404227
  • 55. H. Shulman and J. D. Stasheff, de Rahm theory for BГ, differential topology, foliations and Gelfand-Fuks cohomology, Proc. Topology Sympos. PUC, Rio de Janeiro, 1976, Lecture Notes in Math., vol. 652, Springer-Verlag, Berlin and New York, 1978. MR 520535
  • 56. J. D. Stasheff, H-spaces from a homotopy point of view, Lecture Notes in Math., vol. 161, Springer-Verlag, Berlin and New York, 1970 (Chapter 6. The bar construction spectral sequence.) MR 270372
  • 57. J. D. Stasheff, On extensions of H-spaces, Trans. Amer. Math. Soc. 105 (1962), 126-135. MR 178469
  • 58. W. Thurston, Foliations and groups of diffeomorphism, Bull. Amer. Math. Soc. 80 (1974), 304-307. MR 339267
  • 59. W. Thurston, The theory of foliations of codimension greater than one, Differential Geometry (Proc. Sympos. Pure Math., Stanford, 1973), Amer. Math. Soc., Providence, R. I., 1975. MR 375345
  • 60. W. Thurston, Variations of the Godbillon-Vey invariant in higher dimensions (to appear).
  • 61. W. T. van Est, A generalization of the Cartan-Leray spectral sequence. I, II, Proc. Kon. Neder. Akad. Wetensch. A 61 (1958), 399-413. MR 103467
  • 62. W. T. van Est, Group cohomology and Lie algebra cohomology in Lie groups. I. II. Proc. Kon. Neder. Akad. Wetensch. A 56 = Indag. Math. 15 (1953), 484-504. MR 59285
  • 63. W. T. van Est, On the algebraic cohomology concepts in Lie groups. I, II, Proc. Kon. Neder. Akad. Wetensch. A 58 (1955), 225-233, 286-294. MR 70959
  • 64. W. T. van Est, Une application d'une methode de Cartan-Leray, Proc. Kon. Neder. Akad. Wetensch. A 58 = Indag. Math. 17 (1955), 542-544. MR 73108
  • 65. C. Watkiss, Thesis, Univ. of Toronto, 1975.
  • 66. D. Wigner, Algebraic cohomology of topological groups, Trans. Amer. Math. Soc. 178 (1973), 83-93. MR 338132
  • 67. A. Haefliger, Differentiable cohomology, Cours donné au CIME (1976).
  • 68. H. Samelson, Zum wissenschaftlichen Werk von Heinz Hopf, Jber. Deutsch. Math.-Verein. 78 (1976), 126-146. MR 427001
  • 69. D. Fuchs, Non-trivialité des classes caractéristiques de g-structures. Applications aux classes caractéristiques de feuilletages, C. R. Acad. Sri. Paris 284 (1977), 1017-1019. MR 433469
  • 70. D. Fuchs, Applications aux variations des classes caractéristiques de feuilletages, C. R. Acad. Sci. Paris 284 (1977), 1105-1107. MR 433470

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DOI: https://doi.org/10.1090/S0002-9904-1978-14488-7

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