Related papers: Equivariant blowups of bounded parabolic points

We show that if a (locally compact) group $G$ acts properly on a locally compact $\sigma$-compact space $X$ then there is a family of $G$-invariant proper continuous finite-valued pseudometrics which induces the topology of $X$. If $X$ is…

Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the…

The configuration space of k points on a manifold carries an action of its diffeomorphism group. The homotopy quotient of this action is equivalent to the classifying space of diffeomorphisms of a punctured manifold, and therefore admits…

In this paper, we consider the continuity of the inverse in (strongly) paratopological gyrogroups. The conclusions are established as follows: (1) A compact Hausdorff paratopological gyrogroup $G$ is a topological gyrogroup. (2) A Hausdorff…

We give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger-Gueritaud-Kassel: we show that convex cocompactness in $\mathbb{R} \mathrm{P}^d$ is equivalent to…

Replacing configurations of points by configurations of tubular neighbourhoods (or discs) in a manifold, we are able to define a natural scanning map that is equivariant under the action of the diffeomorphism group of the manifold. We also…

For Schr\"odinger maps from $\R^2\times\R^+$ to the 2-sphere $\S^2$, it is not known if finite energy solutions can form singularities (``blowup'') in finite time. We consider equivariant solutions with energy near the energy of the…

An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology…

Given a group action on a simplicial complex such that each simplex stabiliser admits a cocompact model of classifying space for proper actions, we give conditions implying the existence of a cocompact model of classifying space for proper…

In this paper the some questions of equivariant movability connected with substitution of acting group $G$ on closed subgroup $H$ and with transitions to spaces of $H$-orbits and $H$-fixed points spaces are investigated. In the special case…

Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional integer Heisenberg group. For example any finite index subgroup of SL(3,Z) is such a group. The main result of this paper is that every action of…

We introduce the space of relative orders on a group and show that it is compact whenever the group is finitely generated. We use this to show that if $G$ is a finitely generated group acting by order preserving homeomorphism of on the…

The paper consists of two parts. In the first one we show that a relatively hyperbolic group $G$ splits as a star graph of groups whose central vertex group is finitely generated and the other vertex groups are maximal parabolic subgroups.…

In this paper, we investigate an equivariant homeomorphism of the boundaries $\partial X$ and $\partial Y$ of two proper CAT(0) spaces $X$ and $Y$ on which a CAT(0) group $G$ acts geometrically. We provide a sufficient condition and an…

The aim of this note is to provide a comprehensive treatment of the homotopy theory of $\Gamma$-$G$-spaces for $G$ a finite group. We introduce two level and stable model structures on $\Gamma$-$G$-spaces and exhibit Quillen adjunctions to…

Let $\mathbb{G}$ be a compact Hausdorff group acting on a compact Hausdorff space $X$, $\alpha$ an irreducible $\mathbb{G}$-representation, and $C(X)$ the $C^*$-algebra of complex-valued continuous functions on $X$. We prove that the…

We show sufficient criteria for a group of homeomorphisms acting on a metric space X to extend to one acting on a given compactification of X. We give examples for when this can fail when one of the criteria is not met.

Let $G$ be a connected reductive group acting on an irreducible normal algebraic variety $X$. We give a slightly improved version of local structure theorems obtained by F.Knop and D.A.Timashev that describe an action of some parabolic…

A topological space $G$ is said to be a {\it rectifiable space} provided that there are a surjective homeomorphism $\phi :G\times G\rightarrow G\times G$ and an element $e\in G$ such that $\pi_{1}\circ \phi =\pi_{1}$ and for every $x\in G$…

In this work the equivariant signature of a manifold with proper action of a discrete group is defined as an invariant of equivariant bordisms. It is shown that the computation of this signature can be reduced to its computation on fixed…