Abstract
Many familiar manifolds appear naturally as smooth submanifolds, which are smooth manifolds that are subsets of other smooth manifolds. As you will soon discover, the situation is quite a bit more subtle than the analogous theory of topological subspaces. We begin by defining the most important type of smooth submanifolds, called embedded submanifolds, which have the subspace topology inherited from their containing manifolds. Next, we introduce a more general kind of submanifolds, called immersed submanifolds, which turn out to be the images of injective immersions. At the end of the chapter, we show how the theory of submanifolds can be generalized to the case of submanifolds with boundary.
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© 2013 Springer Science+Business Media New York
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Lee, J.M. (2013). Submanifolds. In: Introduction to Smooth Manifolds. Graduate Texts in Mathematics, vol 218. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9982-5_5
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DOI: https://doi.org/10.1007/978-1-4419-9982-5_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9981-8
Online ISBN: 978-1-4419-9982-5
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