Related papers: Multi-Time Dependent Sprays and Harmonic Maps on $…
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…
We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the…
From a spray space $S$ on a manifold $M$ we construct a new geometric space $P$ of larger dimension with the following properties: 1. Geodesics in $P$ are in one-to-one correspondence with parallel Jacobi fields of $M$. 2. $P$ is complete…
An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which…
An approach to gauge theory in the context of locally conformally flat space-time is described. It is discussed how there are a number of natural principal bundles associated with any given locally conformally flat space-time $X$. The…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
We study the space of oriented genus g subsurfaces of a fixed manifold M, and in particular its homological properties. We construct a "scanning map" which compares this space to the space of sections of a certain fibre bundle over M…
We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric…
Projective structures on topological surfaces support the structure of 2d CFTs with a degree of technical simplification. We propose a complex analytic space $\mathcal{P}_g$ biholomorphic to $T^*_{(1,0)} \mathcal{M}_g$ as a candidate moduli…
The below discussion is in three sections A, B, C, each section in two parts I, II, I representing the standpoint of bundles with connections and II representing the standpoint of prehomogeneous geometries (phg's). In A, our object of study…
Let $S$ be a normal base scheme. The aim of this paper is to study the line bundles on 1-motives defined over $S$. We first compute a d\'evissage of the Picard group of a 1-motive $M$ according to the weight filtration of $M$. This…
We study fiber bundles where the fibers are not a group $G$, but a free $G$-space with disjoint orbits. These bundles closely resemble principal bundles, hence we call them semi-principal bundles. The study of such bundles is facilitated by…
We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of $M$ by a metallic Riemannian structure $(J,g)$ on $M$, providing conditions for their…
We propose a generalization of the classical Tulczyjew triple as a geometric tool in Hamiltonian and Lagrangian formalisms which serves for contact manifolds. The r\^ole of the canonical symplectic structures on cotangent bundles in…
For scalar field theories, such as those EFTs describing the Higgs, it is well-known that the 2-derivative Lagrangian is captured by geometry. That is, the set of operators with exactly 2 derivatives can be obtained by pulling back a metric…
For a principal bundle $P\to M$ equipped with a connection ${\bar A}$, we study an infinite dimensional bundle ${\mathcal P}^{\rm dec}_{\bar A}P$ over the space of paths on $M$, with the points of ${\mathcal P}^{\rm dec}_{\bar A}P$ being…
We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle $M\times G$ by the so-called gauge…
We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by…
We compute the space of global sections for the symmetric power of the tautological bundle on the punctual Hilbert scheme of a complex smooth projective surface.
We classify singular fibres of a projective Lagrangian fibration over codimension one points. As an application, we obtain a canonical bundle formula for a projective Lagrangian fibration over a smooth manifold.