Geodesic
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

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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

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