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...