Related papers: Groups of Circle Diffeomorphisms
The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and…
We extend to the critical (intermediate) regularity several results concerning rigidity for centralizers and group actions on the interval.
A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it…
In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…
In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.
This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.
This text is the preprint version of the concluding chapter for the book New Directions in Locally Compact Groups published by Cambridge University Press in the series Lecture Notes of the LMS. The recent progress on locally compact groups…
We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis of generalized solutions. As an application, we analyze…
In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.
In this short note, we study the bordism problem for group actions on the torus and give examples of groups acting on the torus by diffeomorphisms isotopic to the identity that cannot be extended to an action on a bounding 3-manifold. This…
In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras.
The canonical Brownian motion that P. Malliavin in 1999 and then S. Fang in 2002 constructed lives in the group of Holderian homeomorphisms of the circle. In this paper, we present another way to construct a Brownian motion that lives…
This is a survey article on moduli of affine schemes equipped with an action of a reductive group. The emphasis is on examples and applications to the classification of spherical varieties.
The paper adjoins the book B.Plotkin, S.Vovsi "Varieties of representations of groups", Riga, "Zinatne", 1983, and turns to be, in a sense, its continuation. In the book the varieties of representations had been considered. In the matter of…
A brief review of bicovariant differential calculi on finite groups is given, with some new developments on diffeomorphisms and integration. We illustrate the general theory with the example of the nonabelian finite group S_3.
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…
In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…
This is an almost self-contained monograph (containing some new results) on left-orderable groups which mostly rely on dynamical and probabilistic aspects, but also on geometric, combinatorial, analytic, and topological ones. This new…