Related papers: Designs on the Tautological bundle

The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…

We present a generic construction of finite realisations of amalgamation patterns. An amalgamation pattern is specified by a finite collection of finite template structures together with a collection of partial isomorphisms between them. A…

In this paper we introduce a generalization of Hamiltonian mechanics that replaces configuration spaces, conventionally regarded simply as smooth manifolds, with line bundles over smooth manifolds. Classical observables are then identified…

We give a detailed account of the so-called "universal construction" that aims to extend invariants of closed manifolds, possibly with additional structure, to topological field theories and show that it amounts to a generalization of the…

It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…

We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…

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 address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…

In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…

Let $T$ be a complete, model-complete, geometric dp-minimal $\mathcal{L}$-theory of topological fields of characteristic $0$ and let $T(\partial)$ be the theory of expansions of models of $T$ by a derivation $\partial$. We assume that…

Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame…

We propose a description of T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects…

We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line…

Our aim is to generalize the result that two generic complex line arrangements are equivalent. In fact for a line arrangement A we associate its defining polynomial, the product of a_ix+b_iy+c_i, so that A = (f=0). We prove that the…

We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an…

We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…

We develop a generalized field space geometry for higher-derivative scalar field theories, expressing scattering amplitudes in terms of a covariant geometry on the all-order jet bundle. The incorporation of spacetime and field derivative…

In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…

Unifying several directions of the development of the study of summing multilinear operators between Banach spaces, we construct a general framework that studies, under one single definition, multilinear operators that are summing with…