Regular coverings of a graph or a map admit descriptions in terms of certain group-valued labellings on the graph. Controlling the properties of graphs resulting from such coverings requires to develop a certain type of ‘labelling calculus’. We give a brief outline of the related theory and survey the most important results.

We prove an analog of the classical Hartogs extension theorem for CR L2 functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a question formulated in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds.

The aim of this paper is to give a detailed proof of a comparison of Voevodsky’s categories of geometric motives with and without transfers, respectively. The latter category is defined by means of h-topology introduced by Voevodsky, a topology essentially given by Zariski coverings, finite coverings and blowups.

This paper is a report on the observation that some singular varieties admit Calabi-Yau coverings. We derive a formula for calculating the invariants of the coverings with degeneration methods. By applying these to Takagi’s Q -Fano examples([Ta1], [Ta2]), we construct several Calabi-Yau threefolds with Picard number one. It turns out that at least 22 of them are new.

The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system Takasaki [1] is described. For the standard twofold elliptic coverings the integrable system is written explicitly. The trigonometric degeneration of our construction is presented.

Strongly-cyclic branched coverings of knots are studied by using their (g, 1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups admit geometric g-words cyclic presentations.

We give a decomposition formula for the Bartholdi zeta function of a graph G which is partitioned into some irregular coverings. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of G which is partitioned into some regular coverings. © 2005 Elsevier B.V. All rights reserved.

Let $W$ be a nonorientable $4$-dimensional handlebody without $3$- and $4$-handles. We show that admits Lefschetz fibration over the $2$-disk, whose regular fiber is surface with nonempty boundary. This an analogue of result Harer obtained in orientable case. As corollary, we obtain proof fact every closed $3$-manifold open book decomposition, which was first proved by Berstein Edmonds using br...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.