Abstract
Because the pushforward of a smooth map represents the “best linear approximation” to the map near a given point, we can learn a great deal about the map itself by studying linear-algebraic properties of its pushforward at each point. The most important such property is its rank (the dimension of its image).
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© 2003 Springer Science+Business Media New York
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Lee, J.M. (2003). Submersions, Immersions, and Embeddings. In: Introduction to Smooth Manifolds. Graduate Texts in Mathematics, vol 218. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21752-9_7
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DOI: https://doi.org/10.1007/978-0-387-21752-9_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95448-6
Online ISBN: 978-0-387-21752-9
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