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differential topology

mathematics

Learn about this topic in these articles:

algebraic topology

  • Because both a doughnut and a coffee cup have one hole (handle), they can be mathematically, or topologically, transformed into one another without cutting them in any way. For this reason, it has often been joked that topologists cannot tell the difference between a coffee cup and a doughnut.
    In topology: Differential topology

    Many tools of algebraic topology are well-suited to the study of manifolds. In the field of differential topology an additional structure involving “smoothness,” in the sense of differentiability (see analysis: Formal definition of the derivative), is imposed on manifolds. Since early investigation in…

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work of Milnor

  • John Willard Milnor, 2011.
    In John Willard Milnor

    …1962 for his work in differential topology and the Abel Prize in 2011 for his work in topology, geometry, and algebra.

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