Bulletin of the American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

Continuous cohomology of groups and classifying spaces

Author(s): James D. Stasheff
Journal: Bull. Amer. Math. Soc. 84 (1978), 513-530.
MSC (1970): Primary 55F35, 55F40, 55B35, 55H99; Secondary 17B65, 18H25, 18H10, 57F15
MathSciNet review: 0494071
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References:

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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