Related papers: Continuous quotients for lattice actions on compac…

If a finite p-group G acts continuously on a compact topological manifold M then, with some bound C depending on M alone, G has a subgroup H of index at most C such that the H-action on M has at most C stabilizer subgroups. This result…

We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action…

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)…

Let $X$ be a compact smooth manifold, possibly with boundary. Denote by $X_1,\dots,X_r$ the connected components of $X$. Assume that the integral cohomology of $X$ is torsion free and supported in even degrees. We prove that there exists a…

We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on $M \times \bbS^{n_1} \times...\times \bbS^{n_k}$ for some…

If G is a semidirect product N by H with N normal and finitely generated then G has the property that every finite group is a quotient of some finite index subgroup of G if and only if one of N and H has this property. This has applications…

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

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…

Let $(M, \omega)$ be a connected, compact symplectic manifold equipped with a Hamiltonian $G$ action, where $G$ is a connected compact Lie group. Let $\phi$ be the moment map. In \cite{L}, we proved the following result for $G=S^1$ action:…

We show that any closed biquotient with finite fundamental group admits metrics of positive Ricci curvature. Also, let M be a closed manifold on which a compact Lie group G acts with cohomogeneity one, and let L be a closed subgroup of G…

We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3-manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various…

We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. We define two numbers $r(G)$ and $m(G)$ associated with the roots system of the Lie algebra of a Lie group $G$. If the dimension of the manifold is…

For finitely generated groups $G$ and $H$ equipped with word metrics, a translation-like action of $H$ on $G$ is a free action where each element of $H$ moves elements of $G$ a bounded distance. Translation-like actions provide a geometric…

Let G be a real reductive Lie group and H a closed reductive subgroup of G. We investigate the deformation of "standard" compact quotients of G/H, i.e., of quotients of G/H by discrete subgroups Gamma of G that are uniform lattices in a…

Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m_0, n_0 are the dimensions of the maximal lightlike subspaces tangent to M and…

Consider a Hamiltonian action of a compact Lie group H on a compact symplectic manifold (M,w) and let G be a subgroup of the diffeomorphism group Diff(M). We develop techniques to decide when the maps on rational homotopy and rational…

In the first part of this paper, we let $G$ be a finitely-generated amenable group such that $G/[G, G]$ is torsion-free. We suppose that $G$ acts by homeomorphisms homotopic to the identity on a manifold $M$, and give conditions on $M$…

We prove a number of property (T) permanence results for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of…

In this note we prove the following theorem: Let $G$ be a compact Lie group acting on a compact symplectic manifold $M$ in a Hamiltonian fashion. If $L$ is an $l$-dimensional closed invariant submanifold of $M$, on which the $G$-action is…

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…