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    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 14th 2010

    Wrote two-sided bar construction. There is a lot to add, but I added a query box under the subsection “Delooping machines” which I’m hoping someone like Mike could answer.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeJun 14th 2010

    The movers are coming to our apartment at 8am tomorrow morning, but GoILS is actually available online so perhaps you could answer it yourself. (-:

    The page looks awesome! One thing I think could be made a little more clear is when and where we consider the bar construction as a simplical object, and where we are taking its geometric realization.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 14th 2010

    Thanks! Both for the online reference and for the nice words.

    I agree with your last sentence; the reason I left it open was precisely that I wasn’t quite clear on manipulations like

    Ω|B(S,C 1,Y)||B(ΩS,C 1,Y)|\Omega |B(S, C_1, Y) | \simeq |B(\Omega S, C_1, Y)|

    which I seem to recall May doing. My memory is that there is some hard topology here and there.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJun 14th 2010

    Yes, I think your memory is right.