Related papers: Fiber Bundles and Parseval Frames

Fiber bundles over infinite fields with non-trivial ultra-norms are considered. For them geometric wrap groups are defined and investigated. Besides fields also Cayley-Dickson algebras over fields of characteristic not equal to two are…

We present in the most natural way, that is, in the context of the theory of vector and principal bundles and connections in them, fundamental geometrical concepts related to General Relativity and one of its extensions, the Einstein-Cartan…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

We compare two notions of $G$-fiber bundles and $G$-principal bundles in the literature, with an aim to clarify early results in equivariant bundle theory that are needed in current work of equivariant algebraic topology. We also give…

The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective…

It is known that self-adjoint Hamiltonians with purely discrete eigenvalues can be written as (infinite) linear combination of mutually orthogonal projectors with eigenvalues as coefficients of the expansion. The projectors are defined by…

We show that in a fibration the coformality of the base space implies the coformality of the total space under reasonable conditions, and these conditions can not be weakened. The result is partially dual to the classical work of Lupton…

For each pair of integers g at least 2 and h at least 1, we explicitly construct infinitely many fiber sum and section sum indecomposable genus g surface bundles over genus h surfaces whose total spaces are pairwise homotopy inequivalent.

This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…

Recently, fiber bundle theory has been widely used in the study of the slice regular functions and continuing with this line of research, the present work shows that the quaternionic slice regular Bergman space is the base space of a…

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…

In this paper, we study rational sections of the relative Picard scheme of a linear system on a smooth projective variety. We prove that if the linear system is basepoint-free and the locus of non-integral divisors has codimension at least…

We construct a Petersson-Weil type K\"ahler form on the moduli spaces of Higgs bundles over a compact K\"ahler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature…

Let $M\stackrel\pi \arrow X$ be a principal elliptic fibration over a Kaehler base $X$. We assume that the Kaehler form on $X$ is lifted to an exact form on $M$ (such fibrations are called positive). Examples of these are regular Vaisman…

The moduli space of holomorphic fiber bundles ${\cal M}_n(\Si)$ over a compact Riemann surface $\Si$ is considered. A formula for the regularised determinant and an other for the symplectic form at trivial bundle are proposed.

Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact…

Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph…

Embedding real-world networks presents challenges because it is not clear how to identify their latent geometries. Embedding some disassortative networks, such as scale-free networks, to the Euclidean space has been shown to incur…

We generalize Kontsevich's construction of characteristic classes of fibre bundles with homology sphere fibres and a trivialization of the vertical tangent bundle to framed fibre bundles with closed manifold fibres.

Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1) as a structure group, the other has the quantum group $SU_q(2)$ as a fibre. Both hierarchies are…