The natural affinors on some fiber product preserving gauge bundle functors of vector bundles

Jan Kurek and Wlodzimierz M. Mikulski


Address.
Institute of Mathematics, Maria Curie-Sklodowska University, Lublin, Pl. Marii Curie-Sklodowskiej 1, Poland

Institute of Mathematics, Jagellonian University, Krakow, Reymonta 4, Poland

E-mail. kurek@golem.umcs.lublin.pl

E-mail. mikulski@im.uj.edu.pl

Abstract.
We classify all natural affinors on vertical fiber product preserving gauge bundle functors $F$ on vector bundles. We explain this result for some more known such $F$. We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor $F^*$ dual to $F$ as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.

AMSclassification. 58A05, 58A20.

Keywords. Gauge bundle functors, natural operators, natural transformations, natural affinors, jets.