PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Banach Center Publications

2007 | 76 | 1 | 425-436
Tytuł artykułu

### Linear direct connections

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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, $∇^{τ}$, of a direct connection τ is a linear connection. We determine the curvature tensor of the associated linear connection $∇^{τ}.$
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 specific periodic cyclic cycle $Φ_{*}^{τ},$ manufactured from a direct connection τ, rather than from a smooth linear connection as the Chern-Weil construction does. In addition, we show that the image of the cyclic cycle $Φ_{*}^{τ}$ into the de Rham cohomology (through the A. Connes' isomorphism) coincides with the cycle provided by the Chern-Weil construction applied to the underlying linear connection $∇^{τ}.$
For more details about these constructions, the reader is referred to [M], N. Teleman [Tn.1], [Tn.2], [Tn.3], C. Teleman [Tc], A. Connes [C.1], [C.2] and A. Connes and H. Moscovici [C.M].
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
425-436
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
• Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 93-005 Łódź, Poland
• Mathematical Institute of Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
autor
• Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, 60161 Ancona, Italy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory