Fundamentals of submersions and immersions between infinite-dimensional manifolds

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.

v4: 39 pages, LaTeX, includes a Whitney-type embedding theorem for C^r-regular manifolds modelled on locally convex spaces (Theorem J)

References in corpus (2)

• Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds
• The Frobenius theorem for Banach distributions on infinite-dimensional manifolds and applications in infinite-dimensional Lie theory

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