Topological algebras and abstract differential geometry (Q1963324)

The notions of connection and curvature on principal sheaves, with structural sheaf the sheaf of groups \({\mathcal G}{\mathcal L}(n, {\mathcal A})\), are studied where \({\mathcal A}\) is a sheaf of unital, commutative and associative algebras. Suitable topological algebras provide concrete models of principal sheaves for which an abstract Frobenius integrability condition holds, thus establishing the equivalence between flatness, parallelism and integrability of a connection on them. Some forthcoming papers of the author on this theory are announced.