Immersions, Submersions, and Embeddings

Rajnikant Sinha ()
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Rajnikant Sinha: Magadh University, Department of Mathematics

Chapter Chapter 5 in Smooth Manifolds, 2014, pp 307-430 from Springer

Abstract: Abstract The counterpart of “homeomorphism in topological spaces” and “linear isomorphism in real linear spaces” are the concepts of immersion, submersion, and embedding in smooth manifolds. Because a smooth manifold associates with a topological space together with a collection of linear spaces (i.e., tangent spaces at various points of manifold), there emerges different types of “homomorphisms” among smooth manifolds. Their definitions and various theorems on relationship between immersion, submersion, and embedding constitute a beautiful area of studies. In this chapter, we shall prove some of the important theorems on immersion, submersion, embedding, and its related notions. Definitely, the pace of this chapter is a bit slower for obvious reason.

Keywords: Real Linear Space; Smooth Manifold; Smooth Embedding; Smooth Immersion; Coordinate Basis (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-2104-3_5

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DOI: 10.1007/978-81-322-2104-3_5

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