Related papers: Normally contracting Lie group actions
We show that there are no Anosov actions by (n-1)-dimensional unimodular Lie groups on closed n-dimensional manifolds.
In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that "generic" finitely generated groups have no smooth volume preserving actions on compact manifolds…
We give a complete characterization of Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps. We deduce that every Hamiltonian action of a compact Lie group on a contractible symplectic manifold…
In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids.…
We construct smooth actions of arbitrary compact Lie groups on complex projective spaces, such that the corresponding transformations arising from the group action do not preserve any symplectic structure on the complex projective space.
Necessary or sufficient conditions are presented for the existence of various types of actions of Lie groups and Lie algebras on manifolds.
Topologically and geometrically engaging actions have proved to be useful to obtain rigidity results for semisimple Lie group actions. We show that the action of a simple noncompact Lie group on a compact manifold preserving a unimodular…
Questions of the following sort are addressed: Does a given Lie group or Lie algebra act effectively on a given manifold? How smooth can such actions be? What fxed-point sets are possible? What happens under perturbations? Old results are…
Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion…
We prove vanishing results for unramified stable cohomology of finite groups of Lie type.
We construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact analytic manifold with corners. This generalises the known analogous results in the situation where the real analytic manifold has no…
In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.
Every lattice H in a connected semi-simple Lie group G acts properly discontinuously by isometries on the contractible manifold G/K (K a maximal compact subgroup of G). We prove that if H acts on a contractible manifold W and if either 1)…
This note surveys the well-known structure of G-manifolds and summarizes parts of two papers that have not yet appeared in print: one with joint with J. Bruning and F. W. Kamber, and another with I. Prokhorenkov. In particular, from a given…
Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…
We study compatible actions (introduced by Brown and Loday in their work on the non-abelian tensor product of groups) in the category of Lie algebras over a fixed ring. We describe the Peiffer product via a new diagrammatic approach, which…
We show that for a locally free action of a simply connected nilpotent Lie group on a compact manifold, if every real valued cocycle is cohomologous to a constant cocycle, then the action is parameter rigid. The converse is true if the…
In this paper we classify algebraic Anosov actions of nilpotent Lie groups on closed manifolds, extending the previous results by P. Tomter. We show that they are all nil-suspensions over either suspensions of Anosov actions of Z^k on…
In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor)…
In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…