相关论文: Superconnections and Parallel Transport

Within its traditional range of perversity parameters, intersection cohomology is a topological invariant of pseudomanifolds. This is no longer true once one allows superperversities, in which case intersection cohomology may depend on the…

In this paper, we build the foundation for a theory of controlled rough paths on manifolds. A number of natural candidates for the definition of manifold valued controlled rough paths are developed and shown to be equivalent. The theory of…

We study the problem of defining line bundles over certain non-Hausdorff spaces known as Quantum Tori, motivated by the proposed theory of Real Multiplication for real quadratic fields. We draw analogies from the theory of Line Bundles over…

We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…

Transport through quantum coherent conductors, like atomic junctions, is described by the distribution of conduction channels. Information about the number of channels and their transmission can be extracted from various sources, such as…

Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more…

Conventional quantum routing operates under the entrenched assumption that pathfinding is a prerequisite for routing. This classical-inspired routing model imposes a restricting design option, which prevents scaling the quantumness to the…

In this paper we define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. These are intrinsically related to the Gromov D-operator. As an application we…

Quantum teleportation can be used to define a notion of parallel transport which characterizes the entanglement structure of a quantum state \cite{Czech:2018kvg}. This suggests one can formulate a gauge theory of entanglement. In…

We investigate the hitherto unexplored relation between the superparticle path integral and superfield theory. Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of…

Following the approach of Budzy\'nski and Kondracki, we define covariant differential algebras and connections on locally trivial quantum principal fibre bundles. We also consider covariant derivatives, connection forms and curvatures and…

A tangent category is a categorical abstraction of the tangent bundle construction for smooth manifolds. In that context, Cockett and Cruttwell develop the notion of differential bundle which, by work of MacAdam, generalizes the notion of…

This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it…

A linear section of a double vector bundle is a parallel pair of sections which form a vector bundle morphism; examples include the complete lifts of vector fields to tangent bundles and the horizontal lifts arising from a connection in a…

Colloidal nanoparticles developed as interesting objects to establish two- or three-dimensional super-structures with properties not known from conventional bulk materials. Beyond, the properties can be tuned and quantum effects can be…

This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable conditions, we construct a relative model…

A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…

We review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or…

A supergrid graph is a finite vertex-induced subgraph of the infinite graph whose vertex set consists of all points of the plane with integer coordinates and in which two vertices are adjacent if the difference of their x or y coordinates…

In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…