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تسجيل مستخدم جديدVirtual critical regularity of mapping class group actions on the circle
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We show that if $G_1$ and $G_2$ are non-solvable groups, then no $C^{1,tau}$ action of $(G_1times G_2)*mathbb{Z}$ on $S^1$ is faithful for $tau>0$. As a corollary, if $S$ is an orientable surface of complexity at least three then the critical regularity of an arbitrary finite index subgroup of the mapping class group $mathrm{Mod}(S)$ with respect to the circle is at most one, thus strengthening a result of the first two authors with Baik.
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In this monograph, we give an account of the relationship between the algebraic structure of finitely generated and countable groups and the regularity with which they act on manifolds. We concentrate on the case of one--dimensional manifolds, culmin
ating with a uniform construction of finitely generated groups acting with prescribed regularity on the compact interval and on the circle. We develop the theory of dynamical obstructions to smoothness, beginning with classical results of Denjoy, to more recent results of Kopell, and to modern results such as the $abt$--Lemma. We give a classification of the right-angled Artin groups that have finite critical regularity and discuss their exact critical regularities in many cases, and we compute the virtual critical regularity of most mapping class groups of orientable surfaces.
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ta(mu)$ of any discrete invariant random subgroup $mu$ of the locally compact group $G$ and show that $delta(mu) > frac{d}{2}$ in general and that $delta(mu) = d$ if $mu$ is of divergence type. Whenever $G$ is a rank-one simple Lie group with Kazhdans property $(T)$ it follows that an ergodic invariant random subgroup of divergence type is a lattice. One of our main tools is a maximal ergodic theorem for actions of hyperbolic groups due to Bowen and Nevo.
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