Related papers: On homologically locally connected spaces

We present the example of l^p spaces, where we examine results of topological and algebraic genericity and spaceability. At the end of the paper we include a project with other chains of spaces, mainly of holomorphic functions, as Hardy…

We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $VN(G)$ which is given by $ VN(G) = <VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M. Neufang in their…

Locally symmetric spaces like $SL(n,\mathbb Z)\backslash SL_n(\mathbb R)/SO(n)$ contain immersed compact flat manifolds of dimension equal to the real rank. We give a lower bound for the contribution of these cycles to the homology of…

Following an idea of Bendersky-Gitler, we construct an isomorphism between Anderson's and Arone's complexes modelling the chain complex of a map space. This allows us to apply Shipley's convergence theorem to Arone's model. As a corollary,…

The spaces of Riemannian metrics on a closed manifold $M$ are studied. On the space ${\mathcal M}$ of all Riemannian metrics on $M$ the various weak Riemannian structures are defined and the corresponding connections are studied. The space…

We study three different topologies on the moduli space $\mathscr{H}^{\rm loc}_m$ of equivariant isometry classes of $m$-dimensional locally homogeneous Riemannian spaces. As an application, we provide the first examples of locally…

There are at least two ways to approach the homotopy theory of spaces `at chromatic height $n$': one may localize with respect to $T(n)$-homology or with respect to $v_n$-periodic homotopy groups. It was already observed by Bousfield that…

Let $G$ be a compact group. The existence of certain $G$-homotopy dense subsets in a metrizable $G$-space $X$ plays a fundamental role, as it is equivalent to $X$ being a $G$-ANR. From this perspective, the present paper develops several…

We study the space of oriented genus g subsurfaces of a fixed manifold M, and in particular its homological properties. We construct a "scanning map" which compares this space to the space of sections of a certain fibre bundle over M…

We introduce an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed product construction. We relate these notions to homological…

We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…

We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].

It is shown that each continuous transformation $h$ from Euclidean $m$-space ($m>1$) into Euclidean $n$-space that preserves the equality of distances (that is, fulfils the implication $|x-y|=|z-w|\Rightarrow|h(x)-h(y)|=|h(z)-h(w)|$) is a…

In this paper, we study an interplay between local and global properties of spaces of minimal usco maps equipped with the topology of uniform convergence on compact sets. In particular, for each locally compact space $X$ and metric space…

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

The paper addresses certain topological aspects of Dijkstra's PV-model for parallel computations in concurrency theory. The main result is a computation of the homology of the trace space associated with PV-programs in which access and…

In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding…

We survey some properties of homotopical and homological $Z_n$-sets in topological spaces.

We study homeomorphisms of tiling spaces with finite local complexity (FLC), of which suspensions of $d$-dimensional subshifts are an example, and orbit equivalence of tiling spaces with (possibly) infinite local complexity (ILC). In the…

Let $A$ be a unital commutative associative algebra over a field of characteristic zero, $\k$ be a Lie algebra, and $\z$ a vector space, considered as a trivial module of the Lie algebra $\g := A \otimes \k$. In this paper we give a…