区间上的非光滑局部可指示群作用

一个由区间的C^1同态生成的无忠实作用的局部可指示群

A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval

根据Thurston稳定性定理，闭区间的每个C^1同构群都是局部可指示的（即，每个子组通过Z生成子组因子）。我们证明了，即使对于有限生成群，这种说法的逆是不正确的。更精确地说，我们证明了F_2和Z^2的半直积虽然是局部可指示的，但不嵌入Diff_+^1（] 0，1 [）中. (Here F_2是SL（2，Z）的任意自由子群，它在Z^2上的作用是投射作用。进一步证明了对SL（2，Z）的每个非可解子群G，G与Z^2的半直积不嵌入Diff^1_+（S^1）.

群作用同构问题

The isomorphism problem for group actions

本文研究局部紧群遍历作用的同构问题，证明可指标群的保测遍历作用的共轭关系非Borel，揭示了该分类问题的复杂性。

实直线的概周期同胚群

The group of almost-periodic homeomorphisms of the real line

研究了实直线的概周期同胚群。我们的主要结果是：实直线上无整体不动点的有限生成群的作用共轭于无几乎不动点的几乎周期作用。这就等于说，实直线上的作用可以紧化为紧空间的一维层上的作用，而没有全局不动点。作为应用，我们给出了Witte定理的另一种证明：顺从左序群是局部可指示的。

Amenable groups在线路上运行

Amenable groups that act on the line

设Gamma是一个随机生成的顺从群。使用的想法E Ghys，我们证明，如果伽玛有一个非平凡的，方向保持行动的真正的线，然后伽玛有一个无限的，循环的商。(The相反的是显而易见的）。这意味着如果Gamma在圆上有忠实作用，则Gamma的某个有限指标子群具有所有非平凡的、由它生成的子群都有无限循环幂等的性质。这也意味着每一个左序的顺从群都是局部可指示的。这回答了P Linnell的一个问题。

Rigidity for $C^1$ actions on the interval arising from hyperbolicity I: solvable groups

We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ diffeomorphisms of the closed interval with no global fixed point at the interior, then the action is topologically conjugated to that of an affine group. Moreover, in case of non-Abelian image, we show a rigidity result concerning the multipliers of the homotheties, despite the fact that the conjugacy is not necessarily smooth. Some consequences for non-solvable groups are proposed. In particular, we give new proofs/ex…

Direct products, overlapping actions, and critical regularity

We address the problem of computing the critical regularity of groups of homeomorphisms of the interval. Our main result is that if $H$ and $K$ are two non-solvable groups then a faithful $C^{1,τ}$ action of $H\times K$ on a compact interval $I$ is {\em not overlapping} for all $τ>0$, which by definition means that there must be non-trivial $h\in H$ and $k\in K$ with disjoint support. As a corollary we prove that the right-angled Artin group $(F_2\times F_2)*\mathbb{Z}$ has critical regularity one, which is to say that it admits a faithful $C^1$ action on $I$, but no faithful $C^{1,τ}$ action.…