Related papers: Beyond polarities: Generalizing Maxwell's reciproc…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
General invariants of a geometric mapping of a symmetric affine connection space are obtained in this paper. These invariants are generalizations of the previous obtained basic invariants (see [16]). Moreover, these invariants are related…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
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…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.
The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…
For a projective hypersurface $X \subset \P^n$, the images of the polar maps of degree $k$ are studied. The cohomology class defined by these maps is calculated and classical results on dual varieties are presented as applications.
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many…
Free Maxwell theory on general four-manifolds may, under certain conditions on the background geometry, exhibit holomorphic factorization in its partition function. We show that when this occurs, new discrete symmetries emerge at orbifold…
We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder…
We extend a result proved in \cite{Col} for mirror symmetries of planar systems to measure-preserving non-linear reversibilities of $n$-dimensional systems, dropping the analyticity and nondegeneracy conditions.
We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative term and…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…
We briefly indicate some implications of [1] for the second Lie algebra cohomology of equivariant map algebras and (twisted multi) loop algebras.
This work introduces adelic constructions of direct images of differentials and symbols in the two-dimensional case in the relative situation. In particular, reciprocity laws for relative residues of differentials and symbols are stated and…