The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

The purpose of this paper is to give the algebraic topological background for elliptic cohomology theory and to pose some number theoretic problems suggested by these concepts. Algebraic topologists study functors from the category of spaces to various algebraic categories. In particular there are functors to the category of graded rings called multiplicative generalized cohomology theories. (A...

We introduce an idea for generalization of a local cohomology module, which we call a local cohomology module with respect to a pair of ideals (I, J), and study their various properties. Some vanishing and nonvanishing theorems are given for this generalized version of local cohomology. We also discuss its connection with the ordinary local cohomology.

The organizers of the meeting were Wulf-Dieter Geyer (Erlangen) and Moshe Jarden (Tel Aviv). The 26 talks that were given during the conference fall (roughly) into several categories: 1. Fundamental groups and covers in characteristic p In the rst of two talks on the famous theorem of Safarevi c \Every nite solvable group occurs as a Galois group over a global eld" this result was composed with...

In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

Abstract We consider tilings of the plane with twelve-fold symmetry obtained by cut-and-projection method. compute their cohomology groups using techniques introduced in [ 9]. To do this, we completely describe window, orbits lines under group action, and 0-singularities. The complete family generalized can be described two-parameters it presents a surprisingly rich cohomological structure. put...

We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger–Simons cohomology, and of Ramond–Ramond fields in Type II superstring theory and differential K-theory.

Let $R$ be a commutative Noetherian ring and let $fa$, $fb$ be two ideals of $R$ such that $R/({fa+fb})$ is Artinian. Let $M$, $N$ be two finitely generated $R$-modules. We prove that $H_{fb}^j(H_{fa}^t(M,N))$ is Artinian for $j=0,1$, where $t=inf{iin{mathbb{N}_0}: H_{fa}^i(M,N)$ is not finitelygenerated $}$. Also, we prove that if $DimSupp(H_{fa}^i(M,N))leq 2$, then $H_{fb}^1(H_{fa}^i(M,N))$ i...