Integrability on Direct Limit Banach manifolds

TL;DR

This paper develops a framework for analyzing integrability of distributions on direct limit Banach manifolds, providing criteria for integrability based on local direct limits of Banach anchor ranges.

Contribution

It introduces a new criterion for integrability of distributions on direct limit Banach manifolds, expanding the understanding of their geometric structure.

Findings

Established a criterion for integrability on direct limit Banach manifolds.

Characterized distributions as local direct limits of Banach anchor ranges.

Enhanced the theoretical framework for infinite-dimensional manifold analysis.

Abstract

This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anchor ranges.