Related papers: Natural operations on differential forms

We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we…

We characterize all natural linear operations between spaces of differential forms on contact manifolds. Our main theorem says roughly that such operations are built from some algebraic operators which we introduce and the exterior…

In our previous paper [International Journal of Theoretical Physics, 41 (2002), 1165-1190] we have shown, following the tradition of synthetic differential geometry, that div and rot are uniquely determined, so long as we require that the…

We show how the machine of PROP profiles invented by S. Merkulov can be used to study and classify natural operators in differential geometry. We also give an interpretation of graph complexes arising in this context in terms of…

In exterior calculus on smooth manifolds, the exterior derivative and wedge product are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial…

We explore several notions of $k$-form at a point in a diffeological space, construct bundles of such $k$-forms, and compare sections of these bundles to differential forms. As they are defined locally, our $k$-forms can contain more…

We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal…

We develop a combinatorial theory of vector bundles with connection on locally ordered simplicial complexes. This is a first step towards a discrete exterior calculus for bundle-valued forms. The basic building block is the discrete…

We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local…

In this first paper of a series we study various operads of natural operations on Hochschild cochains and relationships between them.

We describe a topological predual to differential forms constructed as an inductive limit of a sequence of Banach spaces. This subspace of currents has nice properties, in that Dirac chains and polyhedral chains are dense, and its operator…

We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective…

We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of $d$-dimensional manifolds, structured hierarchically so that each $d$-dimensional manifold is contained in the boundary of…

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for…

We sharpen a recent observation by Tim Maudlin: differential calculus is a natural language for physics only if additional structure, like the definition of a Hodge dual or a metric, is given; but the discrete version of this calculus…

In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of…

It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…

We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.

Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…

We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. These operators map primitive forms into…