Related papers: Diffeomorphism groups of critical regularity

We show that, in many situations, a homeomorphism $f$ of a manifold $M$ may be recovered from the (marked) isomorphism class of a finitely generated group of homeomorphisms containing $f$. As an application, we relate the notions of {\em…

If $G$ is a finitely generated group with generators $\{g_1,..., g_s\}$, we say an infinite-order element $f \in G$ is a distortion element of $G$ provided that $\displaystyle \liminf_{n \to \infty} \frac{|f^n|}{n} = 0$, where $|f^n|$ is…

For r at least 3, p at least 2, we classify all actions of the groups Diff^r_c(R) and Diff^r_+(S1) by C^p -diffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of…

Let $G$ be a torsion-free, finitely-generated, nilpotent and metabelian group. In this work we show that $G$ embeds into the group of orientation preserving $C^{1+\alpha}$-diffeomorphisms of the compact interval, for all $\alpha< 1/k$ where…

In this paper we discuss the relationship between groups of diffeomorphisms of spheres and balls. We survey results of a topological nature and then address the relationship as abstract (discrete) groups. We prove that the identity…

We study the regularity of exceptional actions of groups by $C^{1,\alpha}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of…

If $\G$ is a finitely generated group with generators $\{g_1,...,g_j\}$ then an infinite order element $f \in \G$ is a {\em distortion element} of $\G$ provided $\displaystyle{\liminf_{n \to \infty} |f^n|/n = 0,}$ where $|f^n|$ is the word…

We show that the topological groups $Diff_{+}^{1}(I)$ and $Diff_{+}^{1}(\mathbb{S}^1)$ of orientation-preserving $C^1$-diffeomorphisms of the interval and the circle, respectively, admit finitely generated dense subgroups. We also…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

Let $M$ and $N$ be smooth manifolds, with $M$ closed and connected. If the $C^r$--diffeomorphism group of $M$ is elementarily equivalent to the $C^s$--diffeomorphism group of $N$ for some $r,s\in[1,\infty)\cup\{0,\infty\}$, then $r=s$ and…

Let $M$ be a compact one--manifold, and let $\mathrm{Diff}^{1+\mathrm{bv}}(M)$ denote the group of $C^1$ orientation preserving diffeomorphisms of $M$ whose first derivatives have bounded variation. We prove that if $G$ is a group which is…

We classify by numerical invariants the finite subgroups $H$ of a primary abelian group $G$ for which every homomorphism or monomorphism of $H$ into $G$, or every endomorphism of $H$, extends to an endomorphism of $G$. We apply these…

We consider the groups $\operatorname{Diff}_{\mathcal B}(\mathbb R^n)$, $\operatorname{Diff}_{H^\infty}(\mathbb R^n)$, and $\operatorname{Diff}_{\mathcal S}(\mathbb R^n)$ of smooth diffeomorphisms on $\mathbb R^n$ which differ from the…

Let $M$ and $N$ be two closed $C^{\infty}$ manifolds and let $\text{Diff}_c(M)$ denote the group of $C^{\infty}$ diffeomorphisms isotopic to the identity. We prove that any (discrete) group homomorphism between $\text{Diff}_c(M)$ and…

We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P -> M is a smooth principal G-bundle. A `cylinder…

The holomorph of a discrete group $G$ is the universal semi-direct product of $G$. In chapter 1 we describe why it is an interesting object and state main results. In chapter 2 we recall the classical definition of the holomorph as well as…

Let G a group of germs of analytic diffeomorphisms in (C^2,0). We find some remarkable properties supposing that G is finite, linearizable, abelian nilpotent and solvable. In particular, if the group is abelian and has a generic dicritic…

We strengthen the results of \cite{A1}, consequently, we improve the claims of \cite{A2} obtaining the best possible results. Namely, we prove that if a subgroup $\Gamma $ of $\mathrm{Diff}_{+}(I)$ contains a free semigroup on two…

We establish some algebraic properties of the group $\mathrm{Diff}(\mathbb{C}^n,0)$ of germs of analytic diffeomorphisms of $\mathbb{C}^n$, and its formal completion $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$. For instance we describe the…

A group morphism is constructed, which can be realized as the induced morphism of fundamental groups from a holomorphic map between compact Kahler manifolds, but can not be realized by a holomorphic map between smooth projective varieties.…