相关论文: Constructions with bundle gerbes

We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning…

In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…

We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…

We develop a gauge theory or theory of bundles and connections on them at the level of braids and tangles. Extending recent algebraic work, we provide now a fully diagrammatic treatment of principal bundles, a theory of global gauge…

An overview of the accomplishments of constructive quantum field theory is provided.

This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…

In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.

In this work we explore the geometrical interpretation of gauge theories through the formalism of fiber bundles. Moreover, we conduct an investigation in the topology of fiber bundles, providing a proof of the Classification Theorem. In the…

An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…

p-Gerbes are a generalization of bundles that have (p+2)-form field strengths. We develop their properties and use them to show that every theory of p-gerbes can be reinterpreted as a gauge theory containing p-dimensional extended objects.…

Covering space theory is used to construct new examples of buildings.

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

We develop a coarse notion of bundle and use it to understand the coarse geometry of group extensions and, more generally, groups acting on proper metric spaces. The results are particularly sharp for groups acting on (locally finite) trees…

Particular solutions of the Benney equations are constructed. Their properties are discussed.

In this PhD thesis, we have studied certain geometric structures over Lie groupoids and differentiable stacks. This thesis is based on the work [arXiv:2103.04560, arXiv:2012.08447, arXiv:2012.08442, arXiv:1907.00375]. In [arXiv:1907.00375],…

The present-day nuclear structure theory exhibits a great degree of synergy with respect to methods that are used to describe various phenomena in heavy nuclear systems. From few-body methods, through the shell model to mean-field…

Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.

We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with…

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…