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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 29th 2012

    stub for IHL manifold.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJun 29th 2012

    What does it mean that one smooth structure is stronger than another ?

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 30th 2012

    How does this relate to an ILH manifold?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 30th 2012

    What does it mean that one smooth structure is stronger than another ?

    It implies the other.

    How does this relate to an ILH manifold?

    I have seen both permutations used. Which one is more standard?

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 30th 2012

    I always think of the acronym as Inverse Limit of Hilbert, and I’ve never seen IHL, but I’ve not read the literature.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 30th 2012

    Okay, thanks. I have changed it.

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeJun 30th 2012
    • (edited Jun 30th 2012)

    It implies the other.

    Calling it “stronger” or “implies” or XYZ makes no difference to me. Do you have a matematical definition ? For me a smooth structure based on some local models is a maximal class of smoothly compatible atlases based on that class. I also do not understand what is a “sort” in this context (I know sorts in model theory and universal algebra only), as used in the idea section.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 30th 2012

    “of sorts” means: “or alike”. It’s informal language. I don’t feel like putting formal definitions into the entry now. It’s a stub. Maybe somebody else feels inspired to have a go at it. I only wanted the references there to be linked to the term, for the moment..

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeJul 1st 2012

    I rewrote to clarify what I believe that Urs meant in a way that I believe that Zoran will understand. That’s two possibly false beliefs.

    • CommentRowNumber10.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 2nd 2012

    Small edit to ILH manifold: ILH refers to the model spaces (ILH spaces), not the fact the manifold itself is an inverse limit of Hilbert manifolds.

    Though note Andrew’s answer here: http://mathoverflow.net/questions/74064/frechet-manifolds-vs-ilh-manifolds. Apparently there is some subtlety in how the transition functions work, so an ILH manifold is a sort of hybrid beast.