Connections on infinite-dimensional manifolds with corners
This paper extends the study of infinite dimensional manifolds with corners, see, e.g., the earlier works by the authors [\textit{S. Armas-Gómez, J. Margalef Roig, E. Outerelo-Domínguez} and \textit{E. Padrón-Fernández}, Rend. Circ. Mat. Palermo, II. Ser. 44, 45-93 (1995; Zbl 0833.58007); the last three authors, Acta Math. Hung. 72, 105-119 (1996; Zbl 0865.58004)]. The connections on general fiber bundles and vector bundles over such manifolds are the main theme here. About one half of the paper is devoted to the exposition of basic categorical constructions with such bundles; then various types of connections are discussed. As usual in theories including infinite dimensional manifolds, the exposition must be as much coordinate free as possible and then most of the standard features from the finite dimensional cases can be recovered for Banach spaces. The existence theorems are often exceptions, though. The authors prove the existence of linear connections and principal connections at the end of their paper.
scientific article; zbMATH DE number 1115650