Related papers: Uniformly locally o-minimal open core
Generalizing results from \cite{DTk,DU} we study the fine structure of locally minimal (locally) precompact Abelian groups (these are the locally essential subgroups $G$ of LCA groups $L$, i.e., such that $G$ non-trivially meets all…
We provide a characterization of distal ordered abelian groups: An ordered abelian group is distal if and only if, for each prime number $p$, the sizes of ribs with respect to the "valuation" $\mathfrak{s}_p$ are uniformly bounded. This…
We study the behaviour of the topological fundamental group under totally ramified abelian covers (a special case of abelian Galois covers) of complex projective varieties of dimension at least 2.
We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topological 1-basedness -- among the class of t-minimal theories with…
In this paper, we analyse the circumstances in which the adjoint Gabor system is an R-dual of a given Gabor frame in the context of separable uniform time-frequency lattices in locally compact abelian groups. In this regard, we also prove a…
Let $\mathcal{R}$ be an $\mathrm{NIP}$ expansion of $(\mathbb{R},<,+)$ by closed subsets of $\mathbb{R}^n$ and continuous functions $f : \mathbb{R}^m \to \mathbb{R}^n$. Then $\mathcal{R}$ is generically locally o-minimal. It follows that if…
Let $L/K$ be a finite Galois, totally ramified $p$-extension of complete local fields with perfect residue fields of characteristic $p>0$. In this paper, we give conditions, valid for any Galois $p$-group $G={Gal}(L/K)$ (abelian or not) and…
We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal expansion of a real closed field, (G;+) a 2-dimensional group definable in…
In this paper, we study the isomorphism problem for central extensions. More precisely, in some new situations, we provide necessary and sufficient conditions for two central extensions to be isomorphic. We investigate the case when the…
Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under $G$ extends to a linear order on X also invariant under G. We…
We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…
We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…
We study notions such as finite presentability and coherence, for partially ordered abelian groups and vector spaces. Typical results are the following: (i) A partially ordered abelian group G is finitely presented if and only…
Is every locally compact abelian group which admits a Heisenberg central extension isomorphic to the product of a locally compact abelian group and its Pontryagin dual? An affirmative answer is obtained for all the commonly occurring types…
A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…
Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a…
We consider continuous extensions of minimal rotations on a locally connected compact group X by arbitrary locally compact Lie groups and prove regularity (i.e. the existence of orbit closures which project onto the whole basis X) in…
Let $A$ be abelian variety over the function field $K$ of a compact Riemann surface $B$. Fix a model $f \colon \mathcal{A} \to B$ of $A/K$ and a certain effective horizontal divisor $\DD \subset \mathcal{A}$. We give a sufficient condition…
We find conditions which ensure that the topological complexity of a closed manifold $M$ with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on…
This paper addresses the following question of Oort: "Are there any postive dimensional locally symmetric subvarieties of the moduli space of abelian varieties that are contained in the jacobian locus and contain the jacobian of at least…