Related papers: Lim colim versus colim lim. I

Recently, the homology and cohomology of non-k-overlapping discs, or, equivalently, no k-equal subspaces of Euclidean space, were calculated by Dobrinskaya and Turchin. We calculate the homology and cohomology of two classes of more general…

We construct a splitting of the cohomology of configuration spaces of points on a smooth proper variety with a multiplicative Chow--K\"unneth decomposition. Applied to hyperelliptic curves, this shows that the hyperelliptic Torelli group…

Let $R$ be a commutative Noetherian ring, $\mathfrak a$ a proper ideal of $R$ and $N$ a non-zero finitely generated $R$-module with $N\neq \mathfrak a N$. Let $d$ (respectively $c$) be the smallest (respectively greatest) non-negative…

Let $X$ and $Y$ be compact Hausdorff spaces and suppose that there exists a linear continuous surjection $T:C_{p}(X) \to C_{p}(Y)$, where $C_{p}(X)$ denotes the space of all real-valued continuous functions on $X$ endowed with the pointwise…

In a previous paper, we obtained a cohomological obstruction to the existence of compact manifolds locally modelled on a homogeneous space. In this paper, we give a classification of the semisimple symmetric spaces to which this obstruction…

In this paper, we consider coalgebra measurings and the maps induced by them between Hochschild and cyclic homology of algebras. We show that these induced maps are well behaved with respect to the various structures appearing on Hochschild…

It is known that three fundamental questions regarding local Hamiltonians -- approximating the ground state energy (the Local Hamiltonian problem), simulating local measurements on the ground space (APX-SIM), and deciding if the low energy…

On non-K\"ahler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of…

By the Riemann-mapping theorem, one can bijectively map the interior of an $n$-gon $P$ to that of another $n$-gon $Q$ conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of $P$ to those $Q$.…

We show that the disintegration operator on a complete separable metric space along a projection map, restricted to measures for which there is a unique continuous disintegration, is strongly Weihrauch equivalent to the limit operator Lim.…

This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof…

We establish a sharp reciprocity inequality for modulus in compact metric spaces $X$ with finite Hausdorff measure. In particular, when $X$ is also homeomorphic to a planar rectangle, our result answers a question of K. Rajala and M.…

Let X be a simply connected space and k a commutative ring. Goodwillie, Burghelea and Fiedorowiscz proved that the Hochschild cohomology of the singular chains on the pointed loop space HH^{*}S_*(\Omega X) is isomorphic to the free loop…

Let $M$ be a non-zero finitely generated module over a finite dimensional commutative Noetherian local ring $(R,\mathfrak{m})$ with dim$_R(M)=t$. Let $I$ be an ideal of $R$ with grade$(I,M)=c$. In this article we will investigate several…

We provide a machinery for transferring some properties of metrizable $ANR$-spaces to metrizable $LC^n$-spaces. As a result, we show that for complete metrizable spaces the properties $ALC^n$, $LC^n$ and $WLC^n$ coincide to each other. We…

We introduce a model for Hermitian holormorphic Deligne cohomology on a projective algebraic manifold which allows to incorporate singular hermitian structures along a normal crossing divisor. In the case of a projective curve, the…

In this paper we study variations of the Hopf theorem concerning continuous maps $f$ of a compact Riemannian manifold $M$ of dimension $n$ to $\mathbb{R}^n$. We investigate the case when $M$ is a closed convex $n$-dimensional surface and…

K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite…

Given a connected, compact, totally geodesic submanifold Y^m of noncompact type inside a compact locally symmetric space of noncompact type X^n, we provide a sufficient condition that ensures that [Y^m] is nonzero in H_m(X^n; R); in low…

We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a…