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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 29th 2012
   • PermaLink
   Author: Urs
   Format: Markdownstub for _[[IHL manifold]]_.

   stub for IHL manifold.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJun 29th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWhat does it mean that one smooth structure is _stronger_ than another ?

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

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeJun 30th 2012
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexHow does this relate to an ILH manifold?

   How does this relate to an ILH manifold?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 30th 2012
   • PermaLink
   Author: Urs
   Format: Markdown> 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?

   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?

5. • CommentRowNumber5.
   • CommentAuthorDavidRoberts
   • CommentTimeJun 30th 2012
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI always think of the acronym as Inverse Limit of Hilbert, and I've never seen IHL, but I've not read the literature.

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

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJun 30th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownOkay, thanks. I have changed it.

   Okay, thanks. I have changed it.

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeJun 30th 2012
   • (edited Jun 30th 2012)
   • PermaLink
   Author: zskoda
   Format: MarkdownItex> 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.

   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.

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJun 30th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItex"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..

   “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..

9. • CommentRowNumber9.
   • CommentAuthorTobyBartels
   • CommentTimeJul 1st 2012
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI 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.

   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.

10. • CommentRowNumber10.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 2nd 2012
    • PermaLink
    Author: DavidRoberts
    Format: MarkdownItexSmall 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.

    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.