Related papers: Compact weakly symmetric spaces and spherical pair…

We develop the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derive the classification from the cases where $G$ is compact, and then we discuss…

In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing…

We obtain the full classification of coisotropic and polar actions of compact Lie group on irreducible Hermitian symmetric spaces.

Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…

In this paper we take a look at compactly generated weak Hausdorff spaces equipped with an action of a compact Lie group $G$ together with their colimits and homotopy colimits. In particular, we investigate relations between (homotopy)…

Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…

We describe an isomorphism of categories conjectured by Kontsevich. If $M$ and $\widetilde{M}$ are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on $M$ and a suitable version of Fukaya's…

Using Nadler's Geometric Satake Equivalence for real reductive groups, we obtain a description of the equivariant homology of the loop space of splitting-rank symmetric spaces in terms of the relative dual group of the space. The…

We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.

We classify isometric actions of compact Lie groups on quaternionic-K\"ahler projective spaces with vanishing homogeneity rank. We also show that they are not in general quaternion-coisotropic.

In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar…

We obtain a weak homotopy equivalence type result between two topological groups associated with a Kirchberg algebra: the unitary group of the continuous asymptotic centralizer and the loop group of the automorphism group of the…

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…

The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of $[ \mu ,\kappa ]$-compactness.

We show that the locally strongly sober spaces are exactly the coherent sober spaces that are weakly Hausdorff in the sense of Keimel and Lawson. This allows us to describe their Stone duals explicitly. As another application, we show that…

The spaces ${\mathcal S}'/{\mathcal P}$ equipped with the quotient topology and ${\mathcal S}'_\infty$ equipped with the weak-* topology are known to be homeomorphic, where ${\mathcal P}$ denotes the set of all polynomials. The proof is a…

The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…

We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve.

In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.

We prove various classification results for homogeneous locally conformally symplectic manifolds. In particular, we show that a homogeneous locally conformally Kaehler manifold of a reductive group is of Vaisman type, if the normalizer of…