Exponential mapping for Lie groupoids. Applications
Extension of cross-sections and a generalized de Rham theorem.
Fiber product preserving bundle functors as modified vertical Weil functors
We introduce the concept of modified vertical Weil functors on the category of fibred manifolds with -dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil...
Fibering over the Circle within a Bordism Class.
Gauge natural constructions on higher order principal prolongations
Let be a principal prolongation of a principal bundle P → M. We classify all gauge natural operators transforming principal connections on P → M and rth order linear connections on M into general connections on . We also describe all geometric constructions of classical linear connections on from principal connections on P → M and rth order linear connections on M.
Gauge natural prolongation of connections
The main result is the classification of all gauge bundle functors H on the category which admit gauge natural operators transforming principal connections on P → M into general connections on HP → M. We also describe all gauge natural operators of this type. Similar problems are solved for the prolongation of principal connections to HP → P. A special attention is paid to linear connections.
Genera of Ramified Coverings.
Gluing of differentiable spaces and applications.
Higher order jet involution
We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.
Homotopie-Typ hochzusammenhängender ?-Manigfaltigkeiten.
How to define "convex functions" on differentiable manifolds
In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: . if M is a linear manifold, then (M) contains convex functions, . (·) is invariant under diffeomorphisms, . each f ∈ (M) is differentiable on a dense -set, is investigated.
Ideals of the Lie algebras of vector fields
Infinitely many solutions for a boundary value problem with discontinuous nonlinearities.
Infinitesimal differential geometry.
Infinitésimaux et intuitionnisme
Isomorphisms of Lie algebras of vector fields
La trilogie du moment
A toute deux-forme fermée, sur une variété connexe, on associe une famille d’extensions centrales du groupe de ses automorphismes par son tore des périodes. On discute ensuite quelques propriétés de cette construction.
Lifting of linear vector fields to fiber product preserving vertical gauge bundles
We classify all natural operators lifting linear vector fields on vector bundles to vector fields on vertical fiber product preserving gauge bundles over vector bundles. We explain this result for some known examples of such bundles.
Lifting of projectable vector fields to vertical fiber product preserving vector bundles
We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.
Linear direct connections
In this paper we study the geometry of direct connections in smooth vector bundles (see N. Teleman [Tn.3]); we show that the infinitesimal part, , of a direct connection τ is a linear connection. We determine the curvature tensor of the associated linear connection As an application of these results, we present a direct proof of N. Teleman’s Theorem 6.2 [Tn.3], which shows that it is possible to represent the Chern character of smooth vector bundles as the periodic cyclic homology class of a...