In this chapter we analyze the local structure of a smooth map on the basis of its rank. Recall that the rank of a smooth map f : N → M at a point p ∈ N is the rank of its differential at p. Two cases are of special interest: when the map f has maximal rank at a point or constant rank in a neighborhood. Let n = dim N and m = dimM.
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© 2008 Springer Science+Business Media, LLC
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(2008). The Rank of a Smooth Map. In: An Introduction to Manifolds. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-48101-2_11
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DOI: https://doi.org/10.1007/978-0-387-48101-2_11
Publisher Name: Springer, New York, NY
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Online ISBN: 978-0-387-48101-2
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