Related papers: Decomposition theorems for asymptotic property C a…

Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine…

Let $G$ be the generalized free product of two groups with an amalgamated subgroup. We propose an approach that allows one to use results on the residual $p$-finiteness of $G$ for proving that this generalized free product is residually a…

Let $G=\mathop{A\ast B}\limits_C$ be an amalgamated product of finite rank free groups $A$, $B$ and $C$. We introduce atomic measures and corresponding asymptotic densities on a set of normal forms of elements in $G$. We also define two…

We compare several classes of biparameter persistence modules: $\gamma$-products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem, and modules of projective dimension at most 1. We…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…

We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…

We compare finiteness properties of locally compact groups that generalize the properties of being compactly generated and of being compactly presented. Three such families of properties have been proposed: Abels--Tiemeyer's type $C_n$,…

It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically equivalent in a certain sense (which implies, if the…

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…

The notion of a topological Jordan decomposition of a compact element of a reductive p-adic group has proven useful in many contexts. In this paper, we generalise it to groups defined over fairly general discretely-valued fields and prove…

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomorphic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is…

We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing…

All possible products of all elements of an odd order finite group are considered. A set of all such products is called as a K-set. A hypothesis of K-set coincidence of any group of an odd order with its commutant is proposed and the…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end, while allowing for points of incompleteness (or negative scalar curvature) away from this…

Considered herein are the family of nonlinear equations with both dispersive and dissipative homogeneous terms appended. Solutions of these equations that start with finite energia decay to zero as time goes to infinity. We present an…

Let $A$ be a finite-dimensional algebra over a field $k$. We define $A$ to be $\mathbf{C}$-dichotomic if it has the dichotomy property of the representation type on complexes of projective $A$-modules. $\mathbf{C}$-dichotomy implies the…

We construct, in locally compact, second countable, amenable groups, sets with large density that fail to have certain combinatorial properties. For the property of being a shift of a set of measurable recurrence we show that this is…

We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…