We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups. We follow the terminology of [3, 4, 8]. In this paper all topological spaces are Hausdorff. If S is a semigroup then we denote the subset of idempotents of S by E(S). A topological space S that is algebraically a semigroup ...

Introduction Recall that for proper smooth and connected curves of genus g ≥ 2 over an algebraically closed eld of characteristic 0 the structure of the étale fundamental group π g is well known and depends only on the genus g. Namely it is the pro-nite completion of the topological fundamental group of a compact orientable topological surface of genus g. In contrast to this, the structure of t...

Translation surfaces arise in complex analysis, the classification of surface diffeomorphisms and the study of polygonal billiards. In recent years there have been some notable advances in understanding their properties. In particular Calta and McMullen have made significant advances in understanding translation structures in genus 2. This paper is motivated by our desire to reformulate and ext...

I t has recently been shown by Halmos [l ] that there exists a compact topological group which is algebraically isomorphic to the additive group of the real line, an example being given by the character group of the discrete additive group of the rationals. Exploiting his argument a bit further it is easy to see that the most general such example is the direct sum of N replicas of the one alrea...

We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.

Let X be a compact Riemann surface of genus g ≥ 2 and J(X) its Jacobian variety. By the Abel-Jacobi map X → J(X), X is embedded in J(X). The algebraic 1-cycle X −X− in J(X) is homologous to zero. Here we denote by X the image of X under the multiplication map by −1. If X is hyperelliptic, X = X in J(X). For the rest of this paper, suppose g ≥ 3. B. Harris [5] studied the problem whether the cyc...

Let G denote the full subcategory of topological abelian groups consisting of the groups that can be embedded algebraically and topologically into a product of locally compact abelian groups. We show that there is a full coreflective subcategory S of G that contains all locally compact groups and is *-autonomous. This means that for all G,H in S there is an “internal hom” G −◦H whose underlying...