We will show that the singular cohomology groups of a smooth quasi-projective complex variety relative to normal crossing divisor can be described in terms delta-admissible chains. Roughly speaking, chain is simplicial semi-algebraic meeting faces properly. As an application, we Abel-Jacobi map for higher Chow cycles via example, describe Hodge realization polylog constructed by Bloch-Kriz map.

A LieYRep pair consists of a Lie-Yamaguti algebra and its representation. In this paper, we establish the cohomology theory pairs characterize their linear deformations by second group. Then introduce notion relative Rota-Baxter-Nijenhuis structures on pairs, investigate properties, prove that structure gives rise to compatible Rota-Baxter operators under certain condition. Finally, show equiva...

Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field‎. ‎Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...

‎The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations‎, ‎denoted by $Sq^n$‎, ‎between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space‎. ‎Regarding to its vector space structure over $mathbb{Z}_2$‎, ‎it has many base systems and some of the base systems can also be restricted to its sub algebras‎. ‎On the contrary‎, ‎in ...

In general bosonic closed string backgrounds the ghost-dilaton is not the only state in the semi-relative BRST cohomology that can change the dimensionless string coupling. This fact is used to establish complete dilaton theorems in closed string field theory. The ghost-dilaton, however, is the crucial state: for backgrounds where it becomes BRST trivial we prove that the string coupling become...

1. Introduction. D. K. Harrison has recently developed a co-homology theory for commutative algebras over a field [2]. A few key theorems are proved and the results applied to the theory of local rings and eventually to algebraic geometry. The main problem is that both his definitions and proofs require involved calculations. In this paper we define a cohomology theory which (a) relies on more ...

Let Q ∈ C[x1, . . . , xn] be a homogeneous polynomial of degree k > 0. We establish a connection between the Bernstein-Sato polynomial bQ(s) and the degrees of the generators for the top cohomology of the associated Milnor fiber. In particular, the integer uQ = max{i ∈ Z : bQ(−(i+n)/k) = 0} bounds the top degree (as differential form) of the elements in H DR (Q(1), C). The link is provided by t...

In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph flows, using homotopy theoretic methods to construct a virtual fundamental class, and evaluating cohomology classes on this fundamental class. By using similar c...