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Basic Concepts of Manifolds

In: Differential Topology

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  • Amiya Mukherjee

    (Indian Statistical Institute, Statistics and Mathematics Unit)

Abstract

There are two ways one can look at a differentiable manifold. Firstly, it is a topological space with a structure which helps us to define differentiable functions on it, just as a topological structure on a set is designed to define continuous functions on that set. Secondly, it is a topological space which can be obtained by gluing together open subsets of some Euclidean space in a nice way; think, for example, of the surface of a ball or a torus covered with small paper disks pasted together on overlaps without making any crease or fold.

Suggested Citation

  • Amiya Mukherjee, 2015. "Basic Concepts of Manifolds," Springer Books, in: Differential Topology, edition 2, chapter 0, pages 1-42, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-19045-7_1
    DOI: 10.1007/978-3-319-19045-7_1
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