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arXiv · 1502.05795

Fundamentals of submersions and immersions between infinite-dimensional manifolds

Helge Glockner
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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.

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Helge Glockner. 2015-02-20. Fundamentals of submersions and immersions between infinite-dimensional manifolds. https://arxiv.org/abs/1502.05795

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