Related papers: Duality for topological abelian group stacks and T…

We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…

It is a simple fact that a subgroup generated by a subset $A$ of an abelian group is the direct sum of the cyclic groups $\langle a\rangle$, $a\in A$ if and only if the set $A$ is independent. In [5] the concept of an $independent$ set in…

For a locally compact abelian group $G$ a simple proof is given for the known fact that a bounded domain $\Omega$ tiles $G$ with translations by a lattice $\Lambda$ if and only if the set of characters of $G$ indexed by the dual lattice of…

We present sufficient conditions for the existence of matchings in abelian groups and their linear counterparts. These conditions lead to extensions of existing results in matching theory. Additionally, we classify subsets within abelian…

We study the locally compact abelian groups in the class $\mathfrak E_{<\infty}$, that is, having only continuous endomorphisms of finite topological entropy, and in its subclass $\mathfrak E_0$, that is, having all continuous endomorphisms…

The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7].…

In this article we establish some results that allow to deduce the continuity of homomorphisms of (topological) abelian groups from commutative diagrams. In particular, we present a new topological version of the classical Five-Lemma. These…

Is every locally compact abelian group which admits a symplectic self-duality isomorphic to the product of a locally compact abelian group and its Pontryagin dual? Several sufficient conditions, covering all the typical applications are…

We give a direct proof of the local $Tb$ Theorem, in the Euclidean setting, and under the assumption of dual exponents. This Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator, supposing the…

We address two properties for Abelian topological groups: ``every closed subgroup is dually closed'' and ``every closed subgroup is dually embedded.'' We exhibit a pair of topological groups such that each has both of the properties and the…

In this notebook, I present duality theory (or theories) of abelian groups with some categorical and categorical topological flavour. I consider writing this notebook as a longer-term project, and its current content and presentation is…

We investigate topological T-duality in the framework of non-abelian gerbes and higher gauge groups. We show that this framework admits the gluing of locally defined T-duals, in situations where no globally defined ("geometric") T-duals…

We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian…

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

In this paper, we introduce the notions of matching matrices in groups and vector spaces, which lead to some necessary conditions for existence of acyclic matching in abelian groups and its linear analogue. We also study the linear local…

A duality between general partially ordered sets and certain topolgical spaces with two closures is established.

We prove that every finite connected simplicial complex has the homology of the classifying space for some $\mathrm{CAT}(0)$ cubical duality group. More specifically, for any finite simplicial complex $X$, we construct a locally…

We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…

We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological…