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nLab > Latest Changes: microbundle

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2010

    Tim Porter added references to microbundle and I edited the formatting of the entry a bit

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeJan 5th 2010
    Perhaps I should say why I think these objects might warrant more attention. If you look at the sources yu realise that they were one of the central tools in the 1960s in the work that handle smoothing and triangulation. I have a feeling that when it comes to questions on the discretisation of diff geom. that work needs to be taken into account somehow.

  3. Added some info and a reference.

    Anonymous

    diff, v10, current

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeAug 24th 2018

    Added some ’classical’ references.

    diff, v11, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 27th 2021

    Added the original reference. Removed the following discussion to the nForum:

    David Roberts: A couple of years ago I thought of importing topological groupoids to this concept for the following reason: The tangent microbundle M×MM\times M, when MM is a manifold, is the groupoid integrating the tangent bundle TMTM of MM. If we have a general Lie groupoid, we can form the Lie algebroid, which is a very interesting object. If we have a topological groupoid, it seems to me that there should be a microbundle-like object that acts like the algebroid of that groupoid. This should reduce to the tangent microbundle in the case of the codiscrete groupoid = pair groupoid. Perhaps not all topological groupoids would have an associated algebroid, but those wih source and target maps that are topological submersions probably will.

    diff, v15, current

1 to 5 of 5

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