Related papers: Sussmann's orbit theorem and maps

We study flat vector bundles over complex parallelizable manifolds.

Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. For maps like multiplication by an integer modulo 1, such sets have full…

For a given manifold $M$ we consider the non-linear Grassmann manifold $Gr_n(M)$ of $n$-dimensional submanifolds in $M$. A closed $(n+2)$-form on $M$ gives rise to a closed 2-form on $Gr_n(M)$. If the original form was integral, the 2-form…

In recent years a lot of attention has been paid to topological spaces which are a bit more general than smooth manifolds - orbifolds. Orbifolds are intuitively speaking manifolds with some singularities. The formal definition is also…

We present a pair of smooth fiber bundles over the circle with a common $4$-dimensional fiber with the following properties: (1) their total spaces are diffeomorphic to each other; (2) they are isomorphic to each other as topological fiber…

In this paper we describe the complement of real line arrangements in the complex plane in terms of the boundary three-manifold of the line arrangement. We show that the boundary manifold of any line arrangement is a graph manifold with…

This note is but a research announcement, summarizing and explaining results proven and detailed in forthcoming papers. When one studies families of objects over curves, and the objects are parametrized by a Deligne-Mumford stack M, then…

The main purpose this work is to study the minimal fixed point set of fiber-preserving maps for spaces which are fiber bundles over the circle and the fiber is the torus. Using the one-parameter fixed point theory is possible to describe…

A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define…

This paper presents a unified view of manifolds and fiber bundles, which, while superficially different, have strong parallels. It introduces the notions of an m-atlas and of a local coordinate space, and shows that special cases are…

We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.

Seiberg-Witten maps are a well-established method to locally construct noncommutative gauge theories starting from commutative gauge theories. We revisit and classify the ambiguities and the freedom in the definition. Geometrically,…

We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

This study first provides a brief overview of the structure of typical Grassmann manifolds. Then a new type of supergrassmannians is construced using an odd involution in a super ringed space and by gluing superdomains together. Next,…

This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also…

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…

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…

{\it Fold maps} are fundamental tools in generalizing the theory of Morse functions and its application to studies of geometric properties of manifolds. One of the fundamental and important problems in the theory of fold maps is to…