相关论文: On Flat Connections Induced Over Covering Maps

The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor…

The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…

The main goal of this article is to construct some geometric invariants for the topology of the set $\mathcal{F}$ of flat connections on a principal $G$-bundle $P\,\longrightarrow\, M$. Although the characteristic classes of principal…

The authors establish a relation of the theory of varieties with degenerate Gauss maps in projective spaces with the theory of congruences and pseudocongruences of subspaces and show how these two theories can be applied to the construction…

We describe the moduli space of logarithmic rank 2 connections on elliptic curves with 2 poles.

A connection-like objects, termed {\em hom-connections} are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally…

We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…

This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.

Connections and curvings on gerbes are beginning to play a vital role in differential geometry and mathematical physics -- first abelian gerbes, and more recently nonabelian gerbes. These concepts can be elegantly understood using the…

We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle…

Any flat connection on a principal fibre bundle comes from a linear representation of the fundamental group. The noncommutative analog of this fact is discussed here.

Maps from links in thickened surfaces to flat-virtual links help to construct invariants of links using invariants of flat-virtual links. This work is dedicated to investigation of equivalence and invariants of flat-virtual diagrams…

This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.

We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard…

Flip graphs of non-crossing configurations in the plane are widely studied objects, e.g., flip graph of triangulations, spanning trees, Hamiltonian cycles, and perfect matchings. Typically, it is an easy exercise to prove connectivity of a…

In the physics literature, Bilal--Fock--Kogan \cite{BFK} introduced the idea of parabolic reduced flat connections on a surface to give a geometric origin to $W$-algebras. In this paper, we combine these ideas with higher complex…

This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of…

Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…

We study the topology of the SU(2)-representation variety of the compact oriented surface of genus 2 with one boundary component about which the holonomy is a generator of the center of SU(2).

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…