Wrap Groups of Non-Archimedean Fiber Bundles

Abstract

Fiber bundles over infinite fields with non-trivial ultra-norms are considered. For them geometric wrap groups are defined and investigated. Besides fields also Cayley-Dickson algebras over fields of characteristic not equal to two are taken into account. For fibers over them wrap groups are introduced and their structure is investigated. Different classes of smoothness for wrap groups are used. It is demonstrated that generally such groups are infinite dimensional over the corresponding field and totally disconnected groups. That is, they are continuous or differentiable non-archimedean differentiable uniform spaces and the composition $(f,g)\mapsto f^{-1}g$ is continuous or differentiable depending on a class of smoothness of groups. Skew products of wrap groups are studied as well.