Related papers: Horizontal vector fields and Seifert fiberings
Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the…
We define the surface complex for $3$-manifolds and embark on a case study in the arena of Seifert fibered spaces. The base orbifold of a Seifert fibered space captures some of the topology of the Seifert fibered space, so, not…
In this work, we study null hypersurfaces admitting a privileged vector field $\eta$ which is null and tangent at the hypersurface. We derive an identity that relates the deformation tensor of $\eta$ with tensor fields codifying the…
We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of…
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…
We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.
We construct the space of vector fields on quantum groups . Its elements are products of the known left invariant vector fields with the elements of the quantum group itself. We also study the duality between vector fields and 1-forms. The…
A $d$-dimensional invertible topological field theory is a functor from the symmetric monoidal $(\infty,n)$-category of $d$-bordisms (embedded into $\mathbb{R}^\infty$ and equipped with a tangential $(X,\xi)$-structure) which lands in the…
In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds…
We classify global surfaces of section for flows on 3-manifolds defining Seifert fibrations. We discuss branched coverings -- one way or the other -- between surfaces of section for the Hopf flow and those for any other Seifert fibration of…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields.…
In this paper we generalise the theory of real vector bundles to a certain class of non-Hausdorff manifolds. In particular, it is shown that every vector bundle fibred over these non-Hausdorff manifolds can be constructed as a colimit of…
We prove a fibration property for varieties with Hilbert-type properties and give applications to rational points on varieties with nef tangent bundle.
We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot and its…
In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version…
The purpose of this paper is to put into a noncommutative context basic notions related to vector fields from classical differential geometry. The manner of exposition is an attempt to make the material as accessible as possible to…
We extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…
Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…