Related papers: Espaces vectoriels \'echelonn\'es

In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra…

We study higher analogues of effective and effectual topological complexity of spaces equipped with a group action. These are $G$-homotopy invariant and are motivated by the (higher) motion planning problem of $G$-spaces for which their…

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…

In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras.

This paper introduces the notion of fusion action system, an abstraction of the $p$-local data of a finite group acting on a finite set. Fusion action systems are closely connected with the theory of fusion systems; we detail the…

We introduce, for any group $G$, a category $G\Gamma$ such that diagrams $G\Gamma \rightarrow \mathcal{SS}ets$ satisfying a Segal condition correspond to infinite loop spaces with a $G$-action. We also consider diagrams which encode group…

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.

This text focuses on actions on 1-manifolds. We present a (non exhaustive) list of very concrete open questions in the field, each of which is discussed in some detail and complemented with a large list of references, so that a clear…

This is a (very subjective) survey paper for nonspecialists covering group actions on Gromov hyperbolic spaces. The first section is about hyperbolic groups themselves, while the rest of the paper focuses on mapping class groups and…

In this paper, from the viewpoint of the concentration theory of maps, we study a compact group and a L\'{e}vy group action to a large class of metric spaces, such as R-trees, doubling spaces, metric graphs, and Hadamard manifolds.

We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-virtually abelian discontinuous group actions…

We study the interrelation of space functions of groups and the space complexity of the algorithmic word problem in groups.

This paper presents the theory of non-smooth Lie group actions on chains of Banach manifolds. The rigorous functional analytic spaces are given to deal with quotients of such actions. A hydrodynamical example is studied in detail.

We discuss various aspects of isometric group actions on proper metric spaces. As one application, we show that a proper and Weyl transitive action on a euclidean building is strongly transitive on the maximal atlas (the complete apartment…

We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.

We study linear actions of finite groups in small dimensions, up to equivariant birationality.

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals…

We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a…

In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…

We study the sequence entropy for amenable group actions and investigate systematically spectrum and several mixing concepts via sequence entropy both in measure-theoretic dynamical systems and topological dynamical systems. Moreover, we…