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...

Title of Dissertation: Turaev Torsion of 3-Manifolds with Boundary Christopher B. Truman, Doctor of Philosophy, 2006 Dissertation directed by: Professor James A. Schafer Department of Mathematics We study the Turaev torsion of 3-manifolds with boundary; specifically how certain “leading order” terms of the torsion are related to cohomology operations. Chapter 1 consists mainly of definitions an...

We treat a relative version of the main theorem in [F2]: A transcendental approach to Kollár’s injectivity theorem. More explicitly, we give a curvature condition that implies Kollár type cohomology injectivity theorems in the relative setting. To carry out this generalization, we use Ohsawa-Takegoshi’s twisted version of Nakano’s identity.

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...

This article begins with a full description of the quadratic planar vector fields which display two centers. We follow method proposed by Chengzhi Li and provide more detailed analysis different types double centers using classification: Hamiltonian, reversible, Lotka-Volterra, Q4, currently used for fields. also describe completely possible phase portraits their Poincaré compactification. show...

In this work we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The is universal envelope Virasoro Lie relative to locality $N=2$. order obtain result adjust algebraic discrete Morse theory case differential algebras.

In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m ≥ 2. We use Koszul cohomology with it to prove that the relative canonical ring of the fibration is generated in degree up to five.

This paper introduces a new idea in the unital involutive Banach algebras and its closed subset. aims to study cohomology theory of operator algebra. We will algebra as an applied example algebra, be denoted by . The definitions cyclic, simplicial, dihedral group src=image/13426521_01.gif> introduced. presented definition src=image/13426521_14.gif>-relative that i...

We investigate the a matrix-type coring associated to a complete covering of an algebra, its Amitsur complex and propose a definition for the related Čech cohomology relative to the covering.

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category and the relative derived category of modules over the algebra associated to the presheaf are studied. We obtain a generalization of the Special Cohomology Com...