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Math Help - Global Analysis....

  1. #1
    TTB
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    Global Analysis....

    Hi everyone,

    What is global analysis? I've heard it referred to as "analysis on a manifold", but could someone please elaborate further? :-)

    And where does it fit in with the other Analysis's?

    For example, how does it compare to Functional Analysis? Is one a sub-subject of the other? Or are they separate?

    If they are separate, how similar are the techniques, etc, they use?

    Many thanks in advance. :-) x
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  2. #2
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    Quote Originally Posted by TTB View Post
    Hi everyone,

    What is global analysis? I've heard it referred to as "analysis on a manifold", but could someone please elaborate further? :-)

    And where does it fit in with the other Analysis's?

    For example, how does it compare to Functional Analysis? Is one a sub-subject of the other? Or are they separate?

    If they are separate, how similar are the techniques, etc, they use?

    Many thanks in advance. :-) x
    In very broad terms, global analysis is analysis applied to geometry, functional analysis is analysis applied to algebra. They are pretty much separate subjects, with a very different feel to them.
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  3. #3
    TTB
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    Ok thank you. :-)

    So in what way is global analysis different to differential geometry?
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    Quote Originally Posted by TTB View Post
    Ok thank you. :-)

    So in what way is global analysis different to differential geometry?
    Global analysis is a part of the general area of differential geometry. I'm not a specialist in that area myself, but I think that the description here will give you an idea of how it fits in.
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    Generally, Differential Geometry deals with "local" properties (the "differentiable" part) while Gobal Analysis deals with "global" properties or properties in the large.
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