A Tangent Bundle on Diffeological Spaces
نویسندگان
چکیده
We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.
منابع مشابه
Diffeological differential geometry
The main objective for this thesis is the construction of a tensor bundle on a diffeological space X. Thereby getting access to the exterior bundle of antisymmetric tensors on X, and smooth sections here on i.e. differential forms. We shall list certain requirements that any reasonable tensor bundle on a diffeological space should fulfil. And show that the given construction fulfil these requir...
متن کاملSome aspects of cosheaves on diffeological spaces
We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...
متن کاملDifferentiability, Convenient Spaces and Smooth Diffeologies
We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation between the first two is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient if and only if the space and the tangent fibres
متن کاملTangent Bundle of the Hypersurfaces in a Euclidean Space
Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...
متن کاملThe homotopy theory of diffeological spaces
Diffeological spaces are generalizations of smooth manifolds. In this paper, we study the homotopy theory of diffeological spaces. We begin by proving basic properties of the smooth homotopy groups that we will need later. Then we introduce the smooth singular simplicial set S(X) associated to a diffeological space X, and show that when S(X) is fibrant, it captures smooth homotopical properties...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998