Related papers: Multicomplexes on Carnot groups and their associat…
This paper introduces a new construction of subcomplexes associated with a truncated multicomplex. Inspired by the machinery of spectral sequences, this construction yields a collection of interrelated subcomplexes whose differentials…
Inspired by Rumin's work on a subcomplex in sub-Riemannian manifolds which is cohomologically equivalent to the de Rham complex, we present a more general construction that produces subcomplexes from any filtered cochain complex of finite…
In this paper, we present a general construction to extract subcomplexes from two distinct complexes on filtered Riemannian manifolds. The first subcomplex computes the de Rham cohomology of the underlying manifold. On regular subRiemannian…
The Cartier isomorphism allows a nice description of the Bockstein spectral sequence of the de Rham complex over the integers. It is used to compute the integral de Rham cohomology of affine spaces. ----- On decrit la suite spectrale de…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
This paper studies the validity of Stokes' theorem for differential subcomplexes naturally adapted to the noncommutative geometry of positively graded Lie groups, with particular emphasis on Carnot groups. We introduce geometric conditions…
Let ($\Omega^{\ast}(M), d$) be the de Rham cochain complex for a smooth compact closed manifolds $M$ of dimension $n$. For an odd-degree closed form $H$, there are a twisted de Rham cochain complex $(\Omega^{\ast}(M), d+H_\wedge)$ and its…
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
In this paper an alternative definition of the Rumin complex $(E_0^\bullet,d_c)$ is presented, one that relies on a different concept of weights of forms. In this way, the Rumin complex can be constructed on any nilpotent Lie group equipped…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a…
We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal…
We study the de Rham cohomology and the Hodge to de Rham spectral sequence for supervarieties.
We characterize Lie group actions for which there exists, at least locally, an evaluation map that defines a cochain map from the differential complex of invariant forms on a manifold to the De Rham complex for the quotient.
If M is a riemannian manifold, then the inclusion of the complex of coclosed harmonic forms into the de Rham complex induces a linear isomorphism in cohomology. If M has at most countably many connected components, this linear isomorphism…
Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page.…
We present the notion of injective hom-complexity, leading to a connection between the covering number of a group and the sectional number of a group homomorphism, and provide estimates for computing this invariant.
This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…