Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Cohomology
View through CrossRef
Abstract
We quickly browse through simplicial cohomology and spend more time on the de Rham cohomology, a cohomology based on cochain groups of differential forms together with the exterior differential acting as coboundary operator. This latter cohomology theory, which is very well suited to study manifolds and Lie groups, will be instrumental to study the homotopy properties of the Nyquist map from the uncertainty to the return difference matrix viewed as an element of the Lie group GL(ni, C).
Oxford University PressNew York, NY
Title: Cohomology
Description:
Abstract
We quickly browse through simplicial cohomology and spend more time on the de Rham cohomology, a cohomology based on cochain groups of differential forms together with the exterior differential acting as coboundary operator.
This latter cohomology theory, which is very well suited to study manifolds and Lie groups, will be instrumental to study the homotopy properties of the Nyquist map from the uncertainty to the return difference matrix viewed as an element of the Lie group GL(ni, C).
Related Results
Shifted generic cohomology
Shifted generic cohomology
AbstractThe idea that the cohomology of finite groups might be fruitfully approached via the cohomology of ambient semisimple algebraic groups was first shown to be viable in the p...
Coarse Sheaf Cohomology
Coarse Sheaf Cohomology
A certain Grothendieck topology assigned to a metric space gives rise to a sheaf cohomology theory which sees the coarse structure of the space. Already constant coefficients produ...
ℓ∞-Cohomology: Amenability, relative hyperbolicity, isoperimetric inequalities and undecidability
ℓ∞-Cohomology: Amenability, relative hyperbolicity, isoperimetric inequalities and undecidability
We revisit Gersten’s [Formula: see text]-cohomology of groups and spaces, removing the finiteness assumptions required by the original definition while retaining its geometric natu...
Relative cohomology of complexes based on cotorsion pairs
Relative cohomology of complexes based on cotorsion pairs
Let [Formula: see text] be an associative ring with identity. The purpose of this paper is to establish relative cohomology theories based on cotorsion pairs in the setting of unbo...
Spectral sequences
Spectral sequences
Abstract
Spectral sequences play an important role in group cohomology because they provide a means of reducing cohomology in a complex situation to the cohomology o...
Magnitude cohomology
Magnitude cohomology
AbstractMagnitude homology was introduced by Hepworth and Willerton in the case of graphs, and was later extended by Leinster and Shulman to metric spaces and enriched categories. ...
Logarithmic Poisson cohomology: example of calculation and application to prequantization
Logarithmic Poisson cohomology: example of calculation and application to prequantization
In this paper we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure. We prove that the latter induces a representation by logarithmi...
Eisenstein Cohomology
Eisenstein Cohomology
This chapter provides the Eisenstein cohomology. It begins with the Poincaré duality and maximal isotropic subspace of boundary cohomology. Here, the chapter considers the compatib...