no. 1
Second cohomology classes of the group of C 1 -flat diffeomorphisms
[Sur l’un des premiers problèmes de Wiles]
Ishida, Tomohiko1
1 The University of Tokyo Graduate School of Mathematical Sciences Komaba, Meguro-ku ,Tokyo 153-8914 (Japan)
Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 77-85.

We study the cohomology of the group consisting of all C ∞ -diffeomorphisms of the line, which are C 1 -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.

On étudie la cohomologie du groupe des C ∞ -difféomorphismes de la droite, qui sout C 1 -tangents à l’identité à l’origine. On construit deux classes non-triviales de cohomologie réelle de degré deux et un nombre non-dénombrable de classes d’homologie de dimension deux de ce groupe.

DOI : 10.5802/aif.2699
Classification : 58D05, 57S05
Keywords: cohomology of diffeomorphism groups, flat diffeomorphism, Massey product
Mots-clés : semblable banalité autosimilarité logarithmique, loi de Gauß

Ishida, Tomohiko 1

1 The University of Tokyo Graduate School of Mathematical Sciences Komaba, Meguro-ku ,Tokyo 153-8914 (Japan) 
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Ishida, Tomohiko. Second cohomology classes of the group of $C^1$-flat diffeomorphisms. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 77-85. doi : 10.5802/aif.2699. https://aif.centre-mersenne.org/articles/10.5802/aif.2699/

[1] Fukui, Kazuhiko Homologies of the group Diff ∞ (R n ,0) and its subgroups, J. Math. Kyoto Univ., Volume 20 (1980) no. 3, pp. 475-487 | MR | Zbl

[2] Gelʼfand, I. M.; Fuks, D. B. Cohomologies of the Lie algebra of formal vector fields, Izv. Akad. Nauk SSSR Ser. Mat., Volume 34 (1970), pp. 322-337 | MR | Zbl

[3] Goncharova, L. V. The cohomologies of Lie algebras of formal vector fields on the line, Funct. Anal. and Appl., Volume 7 (1973), p. 91-97, 194–203 | DOI | Zbl

[4] Kraines, David Massey higher products, Trans. Amer. Math. Soc., Volume 124 (1966), pp. 431-449 | DOI | MR | Zbl

[5] Millionschikov, D. Algebra of formal vector fields on the line and Buchstaber’s conjecture, Funct. Anal. Appl., Volume 43 (2009), pp. 264-278 | DOI | MR

[6] Takens, Floris Normal forms for certain singularities of vectorfields, Ann. Inst. Fourier (Grenoble), Volume 23 (1973) no. 2, pp. 163-195 Colloque International sur l’Analyse et la Topologie Différentielle (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1972) | DOI | Numdam | MR | Zbl

[7] Weinstein, F. V. Filtering bases: a tool to compute cohomologies of abstract subalgebras of the Witt algebra, Unconventional Lie algebras (Adv. Soviet Math.), Volume 17, Amer. Math. Soc., Providence, RI, 1993, pp. 155-216 | MR | Zbl

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