Related papers: Locally $G$-homogeneous Busemann $G$-spaces

Under Jensen's Diamond Principle, we show how to construct a large compact S-space while having some control over its group of autohomeomorphisms. In particular we can make the space rigid or h-homogeneous (i.e. any two clopen subsets are…

For two not necessarily commutative topological groups G and T, let H(G,T) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G,T) is a…

Let $M$ be a compact Riemannian manifold, and let $G$ be a compact simple Lie group with bi-invariant metric that is not $\operatorname{Sp}(n)$ for $n \geq 8$, $E_{8}$, $F_{4}$, or $G_{2}$. We show that the singular set of any stable…

Here we classify all topological spaces where all bijections to itself are homeomorphisms. As a consequence, we also classify all topological spaces where all maps to itself are continuous. Analogously, we classify all measurable spaces…

The five-dimensional (5D) Riemannian G\"odel-type manifolds are examined in light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are…

We prove that every locally conformally flat metric on a closed, oriented hyperbolic 4-manifold with scalar curvature bounded below by -12 satisfies Schoen's conjecture. We also classify all closed Riemannian 4-manifolds of positive scalar…

We study the higher expansion properties of locally symmetric spaces, with a particular focus on octonionic hyperbolic manifolds. We show that codimension two minimal submanifolds of compact octonionic locally symmetric spaces must have…

This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely when the surface is not the sphere,…

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological…

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

We show that all subvarieties of a quotient of a bounded symmetric domain by a sufficiently small arithmetic discrete group of automorphisms are of general type. This result corresponds through the Green-Griffiths-Lang's conjecture to a…

When does a topological group $G$ have a Hausdorff compactification $bG$ with a remainder belonging to a given class of spaces? In this paper, we mainly improve some results of A.V. Arhangel'ski\v{\i} and C. Liu's. Let $G$ be a non-locally…

We show that for a compact surface without boundary $M$ the set of cw-expansive homeomorphisms is dense in the set of all the homeomorphisms of $M$ with respect to the $C^0$ topology. After this we show that for a generic homeomorphism $f$…

This article records basic topological, as well as homological properties of the space of homomorphisms Hom(L,G) where L is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If L is a free abelian group of…

We show P\'eter Csorba's conjecture that the graph homomorphism complex Hom(C_5,K_{n+2}) is homeomorphic to a Stiefel manifold, the space of unit tangent vectors to the n-dimensional sphere. For this a general tool is developed that allows…

Let G(O_S) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O_S)…

Due to Janet-Cartan's theorem, any analytic Riemannian manifolds can be locally isometrically embedded into a sufficiently high dimensional Euclidean space. However, for an individual Riemannian manifold (M,g), it is in general hard to…

For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with…

In this paper we present some results for a connected infinite graph $G$ with finite degrees where the properties of balls of small radii guarantee the existence of some Hamiltonian and connectivity properties of $G$. (For a vertex $w$ of a…

Gray-Vanhecke conjectured that the volumes of small geodesic balls could determine if the manifold is a space form, and provided a proof for the compact 4-dimensional manifold, and some cases. In this paper, similar results for the…