Related papers: Weak coherence of groups and finite decomposition …
Let A be a commutative ring, and let \a = \frak{a} be a finitely generated ideal in it. It is known that a necessary and sufficient condition for the derived \a-torsion and \a-adic completion functors to be nicely behaved is the weak…
In a general measure space $(X,\mathcal L,\lambda)$, a characterization of weakly null sequences in $L_\infty (X,\mathcal L,\lambda)$ ($u_k \rightharpoonup 0$) in terms of their pointwise behaviour almost everywhere is derived from the…
In deformation-rigidity theory it is often important to know whether certain bimodules are weakly contained in the coarse bimodule. Consider a bimodule $H$ over the group algebra $\mathbb{C}[\Gamma]$, with $\Gamma$ a discrete group. The…
In this paper, we study finiteness criteria for the Gorenstein homological dimension of groups over a commutative ring of finite Gorenstein weak global dimension and provide estimates for the Gorenstein weak global dimension of group rings.…
An $f$-structure, introduced by K. Yano in 1963 and subsequently studied by a number of geometers, is a higher dimensional analog of almost complex and almost contact structures, defined by a (1,1)-tensor field $f$ on a $(2n+p)$-dimensional…
We introduce the weak Haagerup property for locally compact groups and prove several hereditary results for the class of groups with this approximation property. The class contains a priori all weakly amenable groups and groups with the…
The strong shape category of compact metrizable spaces (compacta) is very well-studied; extending it to noncompact spaces, however, introduces computational complexity that makes it hard to work with. The fine shape category, as defined by…
The Weak KAM theory was developed by Fathi in order to study the dynamics of convex Hamiltonian systems. It somehow makes a bridge between viscosity solutions of the Hamilton-Jacobi equation and Mather invariant sets of Hamiltonian systems,…
We introduce a novel topology, called Kernel Mean Embedding Topology, for stochastic kernels, in a weak and strong form. This topology, defined on the spaces of Bochner integrable functions from a signal space to a space of probability…
We define the strong shortcut property for rough geodesic metric spaces, generalizing the notion of strongly shortcut graphs. We show that the strong shortcut property is a rough similarity invariant. We give several new characterizations…
Let $\Gamma$ be a discrete group. Assuming rational injectivity of the Baum-Connes assembly map, we provide new lower bounds on the rank of the positive scalar curvature bordism group and the relative group in Stolz' positive scalar…
The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
A regular semigroup is weakly generated by a set X if it has no proper regular subsemigroups containing X. In this paper, we study the regular semigroups weakly generated by idempotents. We show there exists a regular semigroup FI(X) weakly…
We consider the group $\mathfrak{X}(G)$ obtained from $G\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. Deceptively complicated finitely presented groups arise from…
Using the natural action of $S_\infty$ we show that a countable hereditary class $\mathcal C$ of finitely generated structures has the joint embedding property (JEP) and the weak amalgamation property (WAP) if and only if there is a…
Weak proregularity of an ideal in a commutative ring is a subtle generalization of the noetherian property of the ring. Weak proregularity is of special importance for the study of derived completion, and it occurs quite often in…
A new explicit construction of Cauchy-Fantappi\'e kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary. While not holomorphic in the parameter, the new kernel reflects the complex geometry and the Levi form…
Quantum coherence as an asymmetry relative to a translation group generated by a Hermitian operator, is a necessary resource for the quantum parameter estimation. On the other hand, the sensitivity of the parameter estimation is known to be…
In [2], the authors develop a global correspondence between immersed weakly horospherically convex hypersurfaces $\phi:M^n \to \mathbb{H}^{n+1}$ and a class of conformal metrics on domains of the round sphere $\mathbb{S}^n$. Some of the key…
We introduce the notion of weakly (strongly) infinite real rank for unital $C^{\ast}$-algebras. It is shown that a compact space $X$ is weakly (strongly) infine-dimensional if and only if $C(X)$ has weakly (strongly) infinite real rank.…