Manifolds over algebras and their application to the geometry of jet bundles

Abstract

CONTENTSIntroduction §1. The category of manifolds over algebras §2. Submanifolds generated by invariant submodules §3. Jet bundles as manifolds over local algebras §4. The -prolongation functor on the category of manifolds over algebras §5. Bundles of transversal jets over manifolds with foliations §6. Pseudogroup structures on manifolds over local algebras §7. Fields of geometric objects on jet bundles §8. Higher-order connections on manifoldsReferences