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.
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.
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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
@article{AIF_2024__74_3_1095_0, author = {Triestino, Michele}, title = {Non-smoothability for a class of groups of piecewise linear homeomorphisms of the interval}, journal = {Annales de l'Institut Fourier}, pages = {1095--1108}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {74}, number = {3}, year = {2024}, doi = {10.5802/aif.3626}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3626/} }
TY - JOUR AU - Triestino, Michele TI - Non-smoothability for a class of groups of piecewise linear homeomorphisms of the interval JO - Annales de l'Institut Fourier PY - 2024 SP - 1095 EP - 1108 VL - 74 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3626/ DO - 10.5802/aif.3626 LA - en ID - AIF_2024__74_3_1095_0 ER -
%0 Journal Article %A Triestino, Michele %T Non-smoothability for a class of groups of piecewise linear homeomorphisms of the interval %J Annales de l'Institut Fourier %D 2024 %P 1095-1108 %V 74 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3626/ %R 10.5802/aif.3626 %G en %F AIF_2024__74_3_1095_0
Triestino, Michele. Non-smoothability for a class of groups of piecewise linear homeomorphisms of the interval. Annales de l'Institut Fourier, Volume 74 (2024) no. 3, pp. 1095-1108. doi : 10.5802/aif.3626. https://aif.centre-mersenne.org/articles/10.5802/aif.3626/
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