Related papers: Complexes from complexes
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
In this paper we prove discrete Poincar\'e inequalities that are uniform in the mesh size for the discrete de Rham complex of differential forms developed in [Bonaldi, Di Pietro, Droniou, and Hu, An exterior calculus framework for polytopal…
Given a bounded subanalytic submanifold of $\mathbb{R}^n$, possibly admitting singularities within its closure, we study the cohomology of $L^p$ differential forms having an $L^p$ exterior differential (in the sense of currents) and…
The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…
It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the…
We give some theoretical as well as computational results on Laplace and Maxwell constants. Besides the classical de Rham complex we investigate the complex of elasticity and the complex related to the biharmonic equation and general…
We introduce and study Hodge-de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general…
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…
For smooth manifolds equipped with various geometric structures, we construct complexes that replace the de Rham complex in providing an alternative fine resolution of the sheaf of locally constant functions. In case that the geometric…
We investigate (pseudo)differential forms in the framework of supergeometry. Definitions, basic properties and Cartan calculus (DeRham differential, Lie derivative, inner product, Hodge operator) are presented; the symplectic supermechanics…
Discrete de Rham (DDR) methods provide non-conforming but compatible approximations of the continuous de Rham complex on general polytopal meshes. Owing to the non-conformity, several challenges arise in the analysis of these methods. In…
We characterize two objects by universal property: the derived de Rham complex and Hochschild homology together with its Hochschild-Kostant-Rosenberg (HKR) filtration. This involves endowing these objects with extra structure, built on…
We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan…
A new cohomology, induced by a vector field, is defined on pairs of differential forms ($1$--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an $1$-differentable cohomology of Lichnerowicz…
We develop the formalism of derived divided power algebras, and revisit the theory of derived De Rham and derived crystalline cohomology in this framework. We characterize derived De Rham cohomology of a derived commutative algebra $A$ over…
The de Rham complex arises naturally when studying problems in electromagnetism and fluid mechanics. Stable numerical methods to solve these problems can be obtained by using a discrete de Rham complex that preserves the structure of the…
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation.…
A complex potential is a holomorphic function $\Omega:\mathbb{C} \to \mathbb{C}$ whose real and imaginary parts generate a pair of orthogonal foliations, representing the equipotential lines and the streamlines of $\dot{z} =…
In a beautiful paper Deligne and Illusie proved the degeneration of the Hodge-to-de Rham spectral sequence using positive characteristic methods. In a recent paper Arinkin, C\u{a}ld\u{a}raru and the author of this paper gave a geometric…
As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…