Related papers: Separability in Morse local-to-global groups

We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…

We prove that if K is an infinite stable field whose generic type has weight 1 then K is separably closed. We also obtain partial results when the generic of K has finite weight and when K is strongly stable.

A new proof of the classification for tensor ideal thick subcategories of the bounded derived category, and the stable category, of modular representations of a finite group is obtained. The arguments apply more generally to yield a…

We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.

A graph is split if there is a partition of its vertex set into a clique and an independent set. The present paper is devoted to the splitness of some graphs related to finite simple groups, namely, prime graphs and solvable graphs, and…

We intoduce a local version of the Jordan-Brouwer separation theorem and deduce some global statements, some of which may follow from known results, but the technique is new.

We generalize the classical definition of effectively closed subshift to finitely generated groups. We study classical stability properties of this class and then extend this notion by allowing the usage of an oracle to the word problem of…

We prove that finitely generated virtually free groups are stable in permutations. As an application, we show that almost-periodic almost-automorphisms of labelled graphs are close to periodic automorphisms.

We show that certain subrings of the cohomology of a finite p-group P may be realised as the images of restriction from suitable virtually free groups. We deduce that the cohomology of P is a finite module for any such subring. Examples…

We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable. The construction provides an explicit representation of any such state as a mixture of product…

Separable coordinate systems are introduced in the complex and real four-dimensional flat spaces. We use maximal Abelian subgroups to generate coordinate systems with a maximal number of ignorable variables. The results are presented (also…

A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho=\sum w_K \rho_K'\otimes \rho_K''$, where $\rho_K'$ and $\rho_K''$ are density matrices for the two subsytems, and the positive weights…

Let $\{G_i :i\in\N\}$ be a family of finite Abelian groups. We say that a subgroup $G\leq \prod\limits_{i\in \N}G_i$ is \emph{order controllable} if for every $i\in \mathbb{N}$ there is $n_i\in \mathbb{N}$ such that for each $c\in G$, there…

We prove that the free product of two finitely presented locally tame groups is locally tame and describe many examples of tame subgroups of finitely presented groups. We also include some open problems related to tame subgroups.

We show that an action of a group on a set $X$ is locally finite if and only if $X$ is not equidecomposable with a proper subset of itself. As a consequence, a group is locally finite if and only if its uniform Roe algebra is finite.

The purpose of this paper is to give a sufficient condition for (strong) stability of non-proper smooth functions (with respect to the Whitney $C^\infty$-topology). We show that a Morse function is stable if it is end-trivial at any point…

Let $G$ be a nonabelian group and $n$ a natural number. We say that $G$ has a strict $n$-split decomposition if it can be partitioned as the disjoint union of an abelian subgroup $A$ and $n$ nonempty subsets $B_1, B_2, \ldots, B_n$, such…

A density operator of a bipartite quantum system is called robustly separable if it has a neighborhood of separable operators. Given a bipartite density matrix, its property to be robustly separable is reduced, using the continuous ensemble…

The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive…

Given a category, one may construct slices of it. That is, one builds a new category whose objects are the morphisms from the category with a fixed codomain and morphisms certain commutative triangles. If the category is a groupoid, so that…