Related papers: Differential cohomology (encyclopedia article)
We define the twisted de Rham cohomology and show how to use it to define the notion of an integral of the form $\int g(x) e^{f(x)}dx$ over an arbitrary ring. We discuss also a definition of a family of integrals and some properties of the…
This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).
We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.
Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…
Given a general finite group $G$, there are various finite categories whose cohomology theories are of great interests. Recently Balmer and Grodal gave some new characterizations of the groups of endotrivial modules, via \v{C}ech cohomology…
Motivated by our attempt to understand characteristic classes of Lie groupoids and geometric structures, we are brought back to the fundamentals of the cohomology theories of Lie groupoids and algebroids. One element that was missing in the…
Our constructions provide a systematic way to study cohomology pre-algebraic structures via classical cohomology, simplifying computations and enabling the use of established techniques.
D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.
We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of…
We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more…
Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates…
In this paper we study the homology and cohomology of confguration spaces of two distinct particles on a graph. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra of the…
Diffeology extends differential geometry to spaces beyond smooth manifolds. This paper explores diffeology's key features and illustrates its utility with examples including singular and quotient spaces, and applications in symplectic…
We make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be…