Non-smoothability for a class of groups of piecewise linear homeomorphisms of the interval
[Non-lissabilité pour une classe de groupe d’homéomorphismes linéaires par morceaux de l’intervalle]
Triestino, Michele1
1 Institut de Mathématiques de Bourgogne (IMB, UMR CNRS 5584) Université de Bourgogne 9 av. Alain Savary, 21000 Dijon (France)
Annales de l'Institut Fourier, Online first, 14 p.

Pour une certaine classe de groupes d’homéomorphismes linéaires par morceaux de l’intervalle, on montre qu’ils n’admettent aucune action fidèle sur la droite suffisamment régulière. En s’appuyant sur un travail précédent de Brum, Matte Bon, Rivas, et l’auteur, le nouvel ingrédient est une observation introduite dans un travail récent de Hyde et Tatch Moore, qui permet de ramener le problème aux actions sur le cercle, et ensuite appliquer la théorie d’Herman–Yoccoz.

For a certain class of groups of piecewise linear homeomorphisms of the interval, we prove that they admit no sufficiently regular faithful action on the line. Building on previous work of Brum, Matte Bon, Rivas, and the author, the new ingredient is an observation from a recent work of Hyde and Tatch Moore, which allows to reduce the problem to the case of the circle, and then apply Herman–Yoccoz theory.

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Révisé le :
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DOI : 10.5802/aif.3626
Classification : 37C85, 57M60, 37E05, 37E10
Keywords: Group actions on the real line, locally moving groups, groups of piecewise linear homeomorphisms, Herman–Yoccoz theory, smoothability
Mot clés : Groupes agissant sur la droite, groupes localement mobiles, groupes d’homéomorphismes linéaires par morceaux, théorie d’Herman–Yoccoz, lissabilité
Triestino, Michele 1

1 Institut de Mathématiques de Bourgogne (IMB, UMR CNRS 5584) Université de Bourgogne 9 av. Alain Savary, 21000 Dijon (France) 
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Triestino, Michele. Non-smoothability for a class of groups of piecewise linear homeomorphisms of the interval. Annales de l'Institut Fourier, Online first, 14 p.

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