Topological algebras and abstract differential geometry
Copyright policy )Topological algebras and abstract differential geometry
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.
Differential spaces, curvature of a connection, connection on a principal sheaf, Frobenius theorem, differential triad of an algebra, Generalizations of fiber spaces and bundles in algebraic topology, Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.), Connections (general theory)
Differential spaces, curvature of a connection, connection on a principal sheaf, Frobenius theorem, differential triad of an algebra, Generalizations of fiber spaces and bundles in algebraic topology, Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.), Connections (general theory)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!