相关论文: Synthetic Differential Jet Bundles are Reduced

Tangent categories provide an axiomatic approach to key structural aspects of differential geometry that exist not only in the classical category of smooth manifolds but also in algebraic geometry, homological algebra, computer science, and…

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…

Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…

In this paper we give a brief account of the main aspects of the theory of associated and principal super bundles. As an application, we review the Borel-Weil-Bott Theorem in the super setting, and some results on projective embeddings of…

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing…

The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of…

Mixed boundary conditions are introduced to finite element exterior calculus. We construct smoothed projections from Sobolev de Rham complexes onto finite element de Rham complexes which commute with the exterior derivative, preserve…

Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…

The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general…

We study jet schemes of Newton non-degenerate plane curve singularities. We identify a subgraph of the graph of jet components and show that it can be constructed from walks on the lattice points in the first quadrant of the Cartesian…

The relevant material on differential calculus on graded infinite order jet manifolds and its cohomology is summarized. This mathematics provides the adequate formulation of Lagrangian theories of even and odd variables on smooth manifolds…

We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions.…

We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…

Eliminating the arbitrary coefficients in the equation of a generic plane curve of order $n$ by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to…

Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite…

The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…

Raynaud and Gruson showed that there is a reasonable algebro-geometric notion of family of discrete (infinite-dimensional) vector spaces. The author introduces a notion of family of Tate spaces ("Tate" means "locally linearly compact") and…

We show that there is a fully faithful embedding of the category of manifolds with corners into the Cahiers topos, one of the premier models for Synthetic Differential Geometry. This embedding is shown to have a number of nice properties,…

In this paper we discuss extensions of the canonical quantization procedure in quantum field theories. We focus specifically on S-matrix representation as a T-exponent. This extension involves flat bundles on certain infinite dimensional…

We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…