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Some canonical cohomology classes on groups of volume preserving diffeomorphisms. (English) Zbl 0522.57029


MSC:

57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
58B05 Homotopy and topological questions for infinite-dimensional manifolds
58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
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References:

[1] Augustin Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment. Math. Helv. 53 (1978), no. 2, 174 – 227 (French). · Zbl 0393.58007
[2] R. E. Greene and K. Shiohoma, Diffeomorphisms and volume preserving embeddings of non-compact manifolds, Trans. Amer. Math. Soc. 225 (1979), 403-414. · Zbl 0418.58002
[3] Daniel Henry Gottlieb, Fibre bundles and the Euler characteristic, J. Differential Geometry 10 (1975), 39 – 48. · Zbl 0294.55009
[4] André Haefliger, Homotopy and integrability, Manifolds – Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 133 – 163.
[5] André Haefliger, Cohomology of Lie algebras and foliations, Differential topology, foliations and Gelfand-Fuks cohomology (Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, 1976) Springer, Berlin, 1978, pp. 1 – 12. Lecture Notes in Math., Vol. 652.
[6] André Haefliger, Whitehead products and differential forms, Differential topology, foliations and Gelfand-Fuks cohomology (Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, 1976) Lecture Notes in Math., vol. 652, Springer, Berlin, 1978, pp. 13 – 24.
[7] Steven Hurder, Exotic classes for measured foliations, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 389 – 391. · Zbl 0517.57012
[8] Dusa McDuff, Local homology of groups of volume preserving diffeomorphisms. I, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 4, 609 – 648 (1983). · Zbl 0577.58005
[9] -, Local homology of groups of volume preserving diffeomorphisms III, preprint, 1982. · Zbl 0577.58005
[10] Dusa McDuff, On groups of volume-preserving diffeomorphisms and foliations with transverse volume form, Proc. London Math. Soc. (3) 43 (1981), no. 2, 295 – 320. · Zbl 0411.57028
[11] Guy Rousseau, Difféomorphismes d’une variété symplectique non compacte, Comment. Math. Helv. 53 (1978), no. 4, 622 – 633 (French). · Zbl 0393.53017
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