Fundamentals of submersions and immersions between infinite-dimensional manifolds
Differential Geometry
2016-10-11 v4 Functional Analysis
Abstract
We define submersions f between manifolds M and N modelled on locally convex spaces. If the range N is finite-dimensional or a Banach manifold, then these coincide with the naive notion of a submersion. We study pre-images of submanifolds under submersions and pre-images under mappings whose differentials have dense image. An infinite-dimensional version of the constant rank theorem is provided. We also construct manifold structures on homogeneous spaces G/H of infinite-dimensional Lie groups. Some fundamentals of immersions between infinite-dimensional manifolds are developed as well.
Keywords
Cite
@article{arxiv.1502.05795,
title = {Fundamentals of submersions and immersions between infinite-dimensional manifolds},
author = {Helge Glockner},
journal= {arXiv preprint arXiv:1502.05795},
year = {2016}
}
Comments
v4: 39 pages, LaTeX, includes a Whitney-type embedding theorem for C^r-regular manifolds modelled on locally convex spaces (Theorem J)