Related papers: A connectedness result for commuting diffeomorphis…

We prove that if d is an integer number bigger than 1 and f_1,...,f_d are commuting circle diffeomorphisms respectively of class C^(1+\tau_k), where \tau_1 + ... + \tau_k > 1, then these maps are simultaneously conjugate to rotations…

We prove that the group of diffeomorphisms of the interval $[0,1]$ contains surface groups whose action on $(0,1)$ has no global fix point, is topologically transitive, and such that only countably many points of the interval $(0,1)$ have…

We prove the existence of common fixed points for commuting homeomorphisms of the plane R^2 or the sphere S^2, which preserve a probability measure. For example: some commuting C^1-diffeomorphisms of S^2, which are sufficiently close to the…

Let S be a compact surface - or the interior of a compact surface - and let V be the manifold of cooriented contact elements of S equiped with its canonical contact structure. A diffeomorphism of V that preserves the contact structure and…

We study the group of C^{r}-diffeomorphisms of the closed annulus that are isotopic to the identity. We show that, for r different from 3, the linear space of homogeneous quasi-morphisms on this group is one dimensional. Therefore, the…

We prove that the group of contact diffeomorphisms is closed in the group of all diffeomorphisms in the C^0-topology. By Gromov's alternative, it suffices to exhibit a diffeomorphism that can not be approximated uniformly by contact…

In this announcement, we describe the solution in the C1 topology to a question asked by S. Smale on the genericity of trivial centralizers: the set of diffeomorphisms of a compact connected manifold with trivial centralizer residual in…

We prove that the spaces of $\Cinf$ orientation-preserving actions of $\Z^n$ on $[0,1]$ and nonfree actions of $\Z^2$ on the circle are connected.

In the first part of this text we give a survey of the properties satisfied by the C1-generic conservative diffeomorphisms of compact surfaces. The main result that we will discuss is that a C1-generic conservative diffeomorphism of a…

We prove that if $G\subset\text{Diff}^{1}(\mathbb{R}^2)$ is an Abelian subgroup generated by a family of commuting diffeomorphisms of the plane, all of which are $C^{1}$-close to the identity in the strong $C^{1}$-topology, and if there…

The abstract link L_d of the complex isolated singularity x^2 + y^2 + z^2 + v^{2d} = 0 is diffeomorphic to S^3 \times S^2. We classify the embedded links of these singularities up to regular homotopies precomposed with diffeomorphisms of…

We study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rather interesting. Besides the obvious obstruction given by…

Let $G$ be a $p$-group. We begin to consider the relationship between the structure of the commuting graph and $|G:Z(G)|$. We also build a family of groups whose commuting graphs have more than one connected component whose diameter is at…

Let $f:\mathbb{R}^2 \to \mathbb{R}$ be a real homogeneous polynomial and $S(f)$ be the group of diffeomorphisms $h:\mathbb{R}^2 \to \mathbb{R}^2$ preserving $f$, i.e. $f \circ h = f$. Denote by $S(f,r)$, $(0\leq r \leq \infty)$, the…

In this paper we study the diffeomorphism centralizer of a vector field: given a vector field it is the set of diffeomorphisms that commutes with the flow. Our main theorem states that for a $C^1$-generic diffeomorphism having at most…

Our first main result states that the spectral norm on the group of Hamiltonian diffeomorphisms, introduced in the works of Viterbo, Schwarz and Oh, is continuous with respect to the C^0 topology, when M is symplectically aspherical. This…

We extend to the critical (intermediate) regularity several results concerning rigidity for centralizers and group actions on the interval.

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive…

Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by…

We consider C^r-diffeomorphisms of a compact smooth manifold having a pair of robust heterodimensional cycles where r is a positive integer or infinity. We prove that if certain conditions about the signatures of non-linearities and…