Bulletin of the American Mathematical Society
- Bull. Amer. Math. Soc.
- Volume 84, Number 4 (1978), 513-530.
Continuous cohomology of groups and classifying spaces
Full-text: Open access
Article information
Source
Bull. Amer. Math. Soc., Volume 84, Number 4 (1978), 513-530.
Dates
First available in Project Euclid: 4 July 2007
Permanent link to this document
https://projecteuclid.org/euclid.bams/1183540920
Mathematical Reviews number (MathSciNet)
MR0494071
Zentralblatt MATH identifier
0399.55009
Subjects
Primary: 55F35 55F40 55B35 55H99
Secondary: 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65] 18H25 18H10 57F15
Citation
Stasheff, James D. Continuous cohomology of groups and classifying spaces. Bull. Amer. Math. Soc. 84 (1978), no. 4, 513--530. https://projecteuclid.org/euclid.bams/1183540920
References
- 1. D. Baker, On a class of foliations and the evaluations of their characteristic classes, Thesis, SUNY, Stony Brook, 1976.Zentralblatt MATH: 0346.57007
Mathematical Reviews (MathSciNet): MR438351
Digital Object Identifier: doi:10.1090/S0002-9904-1977-14288-2
Project Euclid: euclid.bams/1183538804 - 2. D. Baker, Differential characters and Borel cohomology, Topology 16 (1977), 441-449.Zentralblatt MATH: 0402.57004
Mathematical Reviews (MathSciNet): MR646086
Digital Object Identifier: doi:10.1016/0040-9383(77)90049-0 - 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.
- 4. A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology 2 (1963), 111-122.Zentralblatt MATH: 0116.38603
Mathematical Reviews (MathSciNet): MR146301
Digital Object Identifier: doi:10.1016/0040-9383(63)90026-0 - 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.
- 7. R. Bott, On the Chern-Weil homomorphism and the continuous cohomology of Lie groups, Advances in Math. 11 (1973), 289-303.Zentralblatt MATH: 0276.55011
Mathematical Reviews (MathSciNet): MR345115
Digital Object Identifier: doi:10.1016/0001-8708(73)90012-1 - 8. R. Bott, Some remarks on continuous cohomology, Proc. Internat. Congress on Manifolds (Tokyo, 1973), Univ. of Tokyo Press, Tokyo, 1975, pp. 161-170.
- 9. R. Bott, H. Shulman and J. Stasheff, On the de Rham theory of classifying spaces, Advances in Math. 20 (1976), 43-56.Zentralblatt MATH: 0342.57016
Mathematical Reviews (MathSciNet): MR402769
Digital Object Identifier: doi:10.1016/0001-8708(76)90169-9 - 10. L. G. Brown, Extensions of topological groups, Pacific J. Math. 39 (1971), 71-78.Zentralblatt MATH: 0241.22004
Mathematical Reviews (MathSciNet): MR307264
Project Euclid: euclid.pjm/1102969770 - 11. H. Cartan, Notions d'algèbre différentielle, Colloq. de Topologie Bruxelles, 1950, pp. 15-27.
- 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.Zentralblatt MATH: 0297.20060
Mathematical Reviews (MathSciNet): MR352333
Digital Object Identifier: doi:10.1007/BF01389727 - 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.
- 15. C. Chevalley and S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124.Zentralblatt MATH: 0031.24803
Mathematical Reviews (MathSciNet): MR24908
Digital Object Identifier: doi:10.1090/S0002-9947-1948-0024908-8 - 16. A. Dold and R. Lashof, Principal quasifibrations and fibre homotopy equivalence of bundles, Illinois J. Math. 3 (1959), 285-305.Zentralblatt MATH: 0088.15301
Mathematical Reviews (MathSciNet): MR101521
Project Euclid: euclid.ijm/1255455128 - 17. J. L. Dupont, Simplicial de Rham cohomology and characteristic classes of flat bundles, Topology 15 (1976), 233-246.Zentralblatt MATH: 0331.55012
Mathematical Reviews (MathSciNet): MR413122
Digital Object Identifier: doi:10.1016/0040-9383(76)90038-0 - 18. D. B. Fuks, Characteristic classes of foliations, Russian Math. Surveys 28 (1973), 1-16.
- 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.
- 20. I. M. Gel'fand and D. B. Fuks, The cohomology of the Lie algebra of formal vector fields, Izvestia 34 (1970), 322-337.
- 21. C. Godbillon, Cohomologie d'algèbres de Lie de champs de vecteurs formels, Séminaire Bourbaki 421 (1972/73).Zentralblatt MATH: 0296.17010
- 22. C. Godbillon and J. Vey, Un invariant des feuilletages de codimension un, C. R. Acad. Sci. Paris 273 (1971), 92.
- 23. W. Greub, S. Halperin and R. Van Stone, Connections, curvature and cohomology. III, Academic Press, New York, 1976, p. 254.
- 24. A. Haefliger, Sur les classes caracteristiques des feuilletages, Séminaire Bourbaki 412 (1972/73).
- 25. A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), 183-194.Zentralblatt MATH: 0196.26901
Mathematical Reviews (MathSciNet): MR263104
Digital Object Identifier: doi:10.1016/0040-9383(70)90040-6 - 26. J. Heitsch, Deformations of secondary characteristic classes, Topology 12 (1973), 381-388.Zentralblatt MATH: 0268.57010
Mathematical Reviews (MathSciNet): MR321106
Digital Object Identifier: doi:10.1016/0040-9383(73)90030-X - 27. J. Heitsch, Independent variation of secondary classes (manuscript).Zentralblatt MATH: 0398.57007
- 28. A. Heller, Principal bundles and group extensions with applications to Hopf algebras, J. Pure Appl. Algebra 3 (1973), 219-250.Zentralblatt MATH: 0275.18012
Mathematical Reviews (MathSciNet): MR327871
Digital Object Identifier: doi:10.1016/0022-4049(73)90011-X - 29. G. P. Hochschild and G. D. Mostow, Cohomology of Lie groups, Illinois J. Math. 6 (1962), 367-401.Zentralblatt MATH: 0111.03302
Mathematical Reviews (MathSciNet): MR147577
Project Euclid: euclid.ijm/1255632500 - 30. S-T Hu, Cohomology rings of compact connected groups and their homogeneous spaces, Ann. of Math (2) 55 (1952), 391-419.Zentralblatt MATH: 0048.25801
Mathematical Reviews (MathSciNet): MR47054
Digital Object Identifier: doi:10.2307/1969641 - 31. S-T Hu, Cohomology theory in topological groups, Michigan Math. J. 1 (1952), 11-59.Zentralblatt MATH: 0048.25802
Mathematical Reviews (MathSciNet): MR51244
Digital Object Identifier: doi:10.1307/mmj/1028989726
Project Euclid: euclid.mmj/1028989726 - 32. F. Kamber and Ph. Tondeur, Characteristic invariants of foliated bundles, Manuscripta Math. 11 (1974), 51-89.Zentralblatt MATH: 0267.57012
Mathematical Reviews (MathSciNet): MR334237
Digital Object Identifier: doi:10.1007/BF01189091 - 33. F. Kamber and Ph. Tondeur, On the linear independence of certain cohomology classes of BГ (preprint).Zentralblatt MATH: 0472.57016
- 34. M. Lazard, Groupes analytiques p-adiques, Publ. Math. IHES 26 (1975).Zentralblatt MATH: 0139.02302
- 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.
- 38. S. Mac Lane, Homology, Die Grundlehren der Math. Wissenschaften, vol. 114, Springer-Verlag, Berlin and New York, 1963.
- 39. S. Mac Lane, Retiring Presidential Address, Bull. Amer. Math. Soc. 82 (1976), 1-40.Zentralblatt MATH: 0324.55001
- 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.
- 41. R. J. Milgram, The bar construction and abelian H-spaces, Illinois J. Math 11 (1967), 242-250.Zentralblatt MATH: 0152.40502
Mathematical Reviews (MathSciNet): MR208595
Project Euclid: euclid.ijm/1256054662 - 42. J. W. Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430-436.Zentralblatt MATH: 0071.17401
Mathematical Reviews (MathSciNet): MR77932
Digital Object Identifier: doi:10.2307/1970012 - 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.
- 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.
- 45. J. C. Moore, Algèbre homologique et homologie des espaces classifiants, Séminaire H. Cartan (1959/60).Zentralblatt MATH: 0115.17205
- 46. S. Morita, A remark on the continuous variation of secondary characteristic classes for foliations (preprint).Zentralblatt MATH: 0343.57013
Mathematical Reviews (MathSciNet): MR442952
Digital Object Identifier: doi:10.2969/jmsj/02920253
Project Euclid: euclid.jmsj/1240433445 - 47. P. S. Mostert, Local cross section in locally compact groups, Proc. Amer. Math. Soc. 4 (1953), 645-649.Zentralblatt MATH: 0103.01801
Mathematical Reviews (MathSciNet): MR56614
Digital Object Identifier: doi:10.1090/S0002-9939-1953-0056614-5 - 48. G. D. Mostow, Cohomology of topological groups and solvmanifolds, Ann. of Math. (2) 73 (1961), 20-48.Zentralblatt MATH: 0103.26501
Mathematical Reviews (MathSciNet): MR125179
Digital Object Identifier: doi:10.2307/1970281 - 49. M. A. Mostow, Continuous cohomology of spaces with two topologies, Mem. Amer. Math. Soc. No. 175 (1976).
- 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.Zentralblatt MATH: 0284.55016
Mathematical Reviews (MathSciNet): MR353298
Digital Object Identifier: doi:10.1016/0040-9383(74)90022-6 - 53. G. Segal, Cohomology of topological groups, Symposia Mathematica IV (1970), 377-387.
- 54. J-P. Serre, Cohomologie Galoisienne, Lecture Notes in Math., vol. 5, Springer-Verlag, Berlin and New York, 1973.
- 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.
- 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.)
- 57. J. D. Stasheff, On extensions of H-spaces, Trans. Amer. Math. Soc. 105 (1962), 126-135.
- 58. W. Thurston, Foliations and groups of diffeomorphism, Bull. Amer. Math. Soc. 80 (1974), 304-307.Zentralblatt MATH: 0295.57014
Mathematical Reviews (MathSciNet): MR339267
Digital Object Identifier: doi:10.1090/S0002-9904-1974-13475-0
Project Euclid: euclid.bams/1183535407 - 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.
- 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.
- 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.
- 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.
- 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.
- 65. C. Watkiss, Thesis, Univ. of Toronto, 1975.
- 66. D. Wigner, Algebraic cohomology of topological groups, Trans. Amer. Math. Soc. 178 (1973), 83-93.Zentralblatt MATH: 0264.22001
Mathematical Reviews (MathSciNet): MR338132
Digital Object Identifier: doi:10.1090/S0002-9947-1973-0338132-7 - 67. A. Haefliger, Differentiable cohomology, Cours donné au CIME (1976).Zentralblatt MATH: 0467.57007
- 68. H. Samelson, Zum wissenschaftlichen Werk von Heinz Hopf, Jber. Deutsch. Math.-Verein. 78 (1976), 126-146.
- 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.
- 70. D. Fuchs, Applications aux variations des classes caractéristiques de feuilletages, C. R. Acad. Sci. Paris 284 (1977), 1105-1107.
American Mathematical Society
- You have access to this content.
- You have partial access to this content.
- You do not have access to this content.
More like this
- On the mod 2 cohomology of the classifying space of the exceptional Lie group $E_{6}$
Kameko, Masaki, Nakagawa, Masaki, and Nishimoto, Tetsu, Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2019 - A second cohomology class of the symplectomorphism group with the discrete topology
Kasagawa, Ryoji, Algebraic & Geometric Topology, 2018 - The proper geometric dimension of the mapping class group
Aramayona, Javier and Martínez-Pérez, Conchita, Algebraic & Geometric Topology, 2014
- On the mod 2 cohomology of the classifying space of the exceptional Lie group $E_{6}$
Kameko, Masaki, Nakagawa, Masaki, and Nishimoto, Tetsu, Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2019 - A second cohomology class of the symplectomorphism group with the discrete topology
Kasagawa, Ryoji, Algebraic & Geometric Topology, 2018 - The proper geometric dimension of the mapping class group
Aramayona, Javier and Martínez-Pérez, Conchita, Algebraic & Geometric Topology, 2014 - On the cycle map of a finite group
Kameko, Masaki, Annals of K-Theory, 2017 - Finite approximations of $p$–local compact groups
Gonzalez, Alex, Geometry & Topology, 2016 - Classifying spaces of twisted loop groups
Baird, Thomas J, Algebraic & Geometric Topology, 2016 - A classifying space for commutativity in Lie groups
Adem, Alejandro and Gómez, José, Algebraic & Geometric Topology, 2015 - Connective $\mathrm{Im}(J)$–theory for cyclic groups
Knapp, Karlheinz, Algebraic & Geometric Topology, 2007 - Mod 2 cohomology of 2-compact groups of low rank
Kaji, Shizuo, Journal of Mathematics of Kyoto University, 2007 - $T$-duality for torus bundles with $H$-fluxes via noncommutative topology. II. The high-dimensional case and the $T$-duality group
Mathai, Varghese and Rosenberg, Jonathan, Advances in Theoretical and Mathematical Physics, 2006