Central S-extensions of the fundamental groupoid of a connected symplectic manifold with an Abelian fundamental group, satisfying some conditon on the universal covering space are computed.

For each Artin group we compute the reduced `cohomology of (the universal cover of) its “Salvetti complex”. This is a CW-complex which is conjectured to be a model for the classifying space of the Artin group. In the many cases when this conjecture is known to hold our calculation describes the reduced `-cohomology of the Artin group.

We introduce an object which in a sense extends the notion of a covering space. Such an object is required to understand the “group” generated by the exponential functions of quadratic forms in the Weyl algebra, and gives in some sense a complexification of the metaplectic group.

Application of covering codes to data embedding improves embedding efficiency and security of steganographic schemes. In this paper, we describe several familes of covering codes constructed using the blockwise direct sum of factorizations. We show that non-linear constructions offer better performance compared to simple linear covering codes currently used by steganographers. Implementation de...

In a recent paper by this author, constructions of linear binary covering codes are considered. In this work, constructions and techniques of the earlier paper are developed and modified for q-ary linear nonbinary covering codes, q 2 3, and new constructions are proposed. The described constructions design an infinite family of codes with covering radius R based on a starting code of the same c...

We show that if a knot exterior satis"es certain conditions, then it has "nite cyclic coverings with arbitrarily large numbers of nontrivial algebraic components in their SL(2, ) character varieties (Theorem A). As an example, these conditions hold for hyperbolic punctured torus bundles over the circle (Theorem B). We investigate in more detail the "nite cyclic covers of the "gure-eight knot ex...

In this paper we analyse the complexity of boolean functions takes value 0 on a sufficiently small number of points. For many functions this leads to the analysis of a single function attains 0 only on unsigned representation of numbers from 1 to d for various d. Here we obtain a tight bounds on the DNF complexity of complete functions in terms of the number of literals and conjunctions. The me...

We write down the chain complex C∗ of the universal cover of the torus, and indicate how to do likewise for any 2-dimensional CW complex arising as the 2-skeleton of a K(G, 1). We exhibit a contracting chain homotopy for this chain complex, and again explain how to do so for the chain complex of the universal cover of our more general CW complex. This yields a contracting homotopy for the tenso...

let $gamma(s_n)$ be the minimum number of proper subgroups‎ ‎$h_i, i=1‎, ‎dots‎, ‎l $ of the symmetric group $s_n$ such that each element in $s_n$‎ ‎lies in some conjugate of one of the $h_i.$ in this paper we‎ ‎conjecture that $$gamma(s_n)=frac{n}{2}left(1-frac{1}{p_1}right)‎ ‎left(1-frac{1}{p_2}right)+2,$$ where $p_1,p_2$ are the two smallest primes‎ ‎in the factorization of $ninmathbb{n}$ an...

In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects and can sometimes be more efficient to deal with problems in the real world. Through extending partitions to cover...