Related papers: Concentration of maps and group action

In this chapter, we investigate directional entropy for semigroup actions generated by one-dimensional linear cellular automata (LCAs) and the shift transformation on the compact metric space $\mathbb{Z}_m^{\mathbb{N}}$. This work provides…

We study the classifying space of a twisted loop group $L_{\sigma}G$ where $G$ is a compact Lie group and $\sigma$ is an automorphism of $G$ of finite order modulo inner automorphisms. Equivalently, we study the $\sigma$-twisted adjoint…

We apply compact group theory to obtain some model-theoretic results about the relativized Lascar Galois group of a strong type.

With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…

We prove a quantitative version of the classical Tits' alternative for discrete groups acting on packed Gromov-hyperbolic spaces supporting a convex geodesic bicombing. Some geometric consequences, as uniform estimates on systole, diastole,…

We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ differentiable map from a Hilbert space to a finite-dimensional…

We develop the foundations of the theory of relatively geometric actions of relatively hyperbolic groups on CAT(0) cube complexes, a notion introduced in our previous work [5]. In the relatively geometric setting we prove: full relatively…

Let $M$ be a monoid and $G:\mathbf{Mon} \to \mathbf{Grp}$ be the group completion functor from monoids to groups. Given a collection $\mathcal{X}$ of submonoids of $M$ and for each $N\in \mathcal{X}$ a collection $\mathcal{Y}_N$ of…

Let $K$ be a compact connected Lie group acting unitarily on a finite-dimensional complex vector space $V$. One calls this a {\em multiplicity-free} action whenever the $K$-isotypic components of $\C[V]$ are $K$-irreducible. We have shown…

Image processing problems in general, and in particular in the field of single-particle cryo-electron microscopy, often require considering images up to their rotations and translations. Such problems were tackled successfully when…

We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact quantum metric space in a natural way. We…

We construct a compactification of the moduli space of twisted holomorphic maps with varying complex structure and bounded energy. For a given compact symplectic manifold $X$ with a compatible complex structure and a Hamiltonian action of…

Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to define a new notion of pseudo-metric on the space of matrices. Moreover, we show that such…

An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on…

Via a compactification of the cleavage operad, we describe two actions on the mapping spaces from spheres into compact, oriented manifolds. The map from the compactified version of the cleavage operad provides a version of intersection…

Let $\Gamma$ be a finitely generated group which admits an action by homeomorphisms on a compact metrizable space $X$. We show that there is a metric on $X$ defining the original topology such that for this metric, the action is by…

It is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety -- not finitary, but bounded by $\aleph_1$. In this note we show that the dual of the category of partially ordered…

We generalise Atiyah and Hirzebruch's vanishing theorem for actions by compact groups on compact Spin-manifolds to possibly noncompact groups acting properly and cocompactly on possibly noncompact Spin-manifolds. As corollaries, we obtain…

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…

The purpose of this paper is to study the action of the mapping class group on the moduli space of representations of the fundamental group of a non-orientable surface into SU(2). The action is shown to be ergodic with respect to a natural…