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Cocycles d'Euler et de Maslov

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Conclusion

Nous espérons avoir convaincu le lecteur qu'il peut être utile de considérer la classe de Maslov comme une classe bornée. Dans [Gh], nous avons montré que la classe d'Euler bornée pour un groupe d'homéomorphismes directs du cercle rend compte de la dynamique topologique de ce groupe. Existe-t-il un résultat analogue pour Sp(2n,ℝ)? En d'autres termes, soit Γ un groupe discret et ϱ1, ϱ2 deux représentations de Γ dans Sp(2n,ℝ). On suppose que les cocycles ϱ *1 σ et ϱ *2 σ définissent la même classe bornée. Que peut-on en conclure sur ϱ1 et ϱ2?

Par ailleurs, l'article [At l] traite aussi d'invariants sur SL(2,ℤ) différents de ceux que nous avons considérés, comme par exemple les fonctionsL de Shimizu. Est-il possible de les faire rentrer naturellement dans notre cadre?

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Author notes

  1. J. Barge

    Present address: Centre de Mathématiques, URA 169 CNRS, Ecole polytechnique, F-91128, Palaiseau Cedex, France

Authors and Affiliations

  1. Institut Fourier, Université de Grenoble I, BP 74, F-38402, St. Martin d'Hères, France

    J. Barge

  2. UMR 128 du CNRS, E.N.S. Lyon, 46, Allée d'Italie, F-69364, Lyon Cedex, France

    E. Ghys

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  1. J. Barge
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Barge, J., Ghys, E. Cocycles d'Euler et de Maslov. Math. Ann. 294, 235–265 (1992). https://doi.org/10.1007/BF01934324

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