Related papers: Subexponential growth and $C^1$ actions on one-man…

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…

The mapping class group $\mathrm{Mod}_{g, 1}$ of a surface with one marked point can be identified with an index two subgroup of $\mathrm{Aut}(\pi_1 \Sigma_g)$. For a surface of genus $g \geq 2$, we show that any action of $\mathrm{Mod}_{g,…

Extending well-known results on surfaces, we give bounds on the cohomological action of automorphisms of compact K\"ahler threefolds. More precisely, if the action is virtually unipotent we prove that the norm of $(f^n)^*$ grows at most as…

We show that every interaction group extending an action of an Ore semigroup by injective unital endomorphisms of a C*-algebra, admits a dilation to an action of the corresponding enveloping group on another unital C*-algebra, of which the…

For any abelian compact Lie group $G$, we introduce a family of $G$-stratified pseudomanifolds, whose main feature is the preservation of the orbit spaces in the category of stratified pseudomanifolds. Which generalize a previous definition…

Definition of a smooth action of a CQG on a compact, smooth manifold is given and studied. It is shown that a smooth action is always injective. Furthermore A necessary and sufficient condition for a lift of the smooth action as a bimodule…

In this work one shows that given a connected $C^\infty$-manifold $M$ of dimension $\geq 2$ and a finite subgroup $G\subset \Diff(M)$, there exists a complete vector field $X$ on $M$ such that its automorphism group equals $G\times…

For a group $G$ and $\omega\in Z^{3}(G, \text{U}(1))$, an $\omega$-anomalous action on a C*-algebra $B$ is a $\text{U}(1)$-linear monoidal functor between 2-groups $\text{2-Gr}(G, \text{U}(1), \omega)\rightarrow \underline{\text{Aut}}(B)$,…

We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…

In this paper we establish a connection between categorical closedness and topologizability of semigroups. In particular, for a class $\mathsf T_{\!1}\mathsf S$ of $T_1$ topological semigroups we prove that a countable semigroup $X$ with…

The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…

Let $G$ be a finitely generated group acting faithfully and properly discontinuously by homeomorphisms on a planar surface $X \subseteq \mathbb{S}^2$. We prove that $G$ admits such an action that is in addition co-compact, provided we can…

It is well-known by the work of Hsiang and Kleiner that every closed oriented positively curved 4-dimensional manifold with an effective isometric S^1-action is homeomorphic to S^4 or CP^2. As stated, it is a topological classification. The…

In a previous article, analytic 1-submanifolds had been classified w.r.t. their symmetry under a given regular and separately analytic Lie group action on an analytic manifold. It was shown that such an analytic 1-submanifold is either free…

We consider pairs (V,H) of subgroups of a connected unipotent complex Lie group G for which the induced VxH-action on G by multiplication from the left and from the right is free. We prove that this action is proper if the Lie algebra g of…

In this paper, we prove a Galois correspondence for compact group actions on C*-algebras in the presence of a commuting minimal action. Namely, we show that there is a one to one correspondence between the C*-subalgebras that are globally…

Let G be a Lie group acting by diffeomorphisms on a manifold M and consider the image of T[1]G and T[1]M, of G and M respectively, in the category of differential graded manifolds. We show that the obstruction to lift the action of T[1]G on…

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we…

Given an action of a groupoid by isomorphisms on a Fell bundle (over another groupoid), we form a semidirect-product Fell bundle, and prove that its $C^{*}$-algebra is isomorphic to a crossed product.

We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is $C^1$ differentiable. As an application, we give a straightforward definition of the integration $\int_X \omega$ over a compact…