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Manifolds

In: Differential Manifolds

Author

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  • Serge Lang

    (Yale University, Department of Mathematics)

Abstract

Starting with open subsets of Banach spaces, one can glue them together with C p -isomorphisms. The result is called a manifold. We begin by giving the formal definition. We then make manifolds into a category, and discuss special types of morphisms. We define the tangent space at each point, and apply the criteria following the inverse function theorem to get a local splitting of a manifold when the tangent space splits at a point.

Suggested Citation

  • Serge Lang, 1985. "Manifolds," Springer Books, in: Differential Manifolds, chapter 0, pages 21-40, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4684-0265-0_2
    DOI: 10.1007/978-1-4684-0265-0_2
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