Product preserving gauge bundle functors on all principal bundle homomorphisms

• Autorzy: Włodzimierz M. Mikulski
• Języki publikacji: EN

Abstrakty

EN

Let 𝓟𝓑 be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on 𝓟𝓑 and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on 𝓟𝓑 admits a prolongation of principal connections to general ones. We also prove a "reduction" theorem for prolongations of principal connections into principal ones by means of Weil functors. We observe that there exist plenty of such prolongations. In Appendix, we classify the natural operators lifting vector-valued 1-forms (or vector-valued maps) to vector-valued 1-forms on Weil bundles.

Kategorie tematyczne

• 58A05: Differentiable manifolds, foundations
• 58A32: Natural bundles
• 58A20: Jets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2011
• Tom: 101
• Numer: 2
• Strony: 163-207

Daty

wydano

2011

Twórcy

autor

Włodzimierz M. Mikulski

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ap101-2-6