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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 14th 2010
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   Author: Todd_Trimble
   Format: MarkdownItexWrote [[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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJun 14th 2010
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   Author: Mike Shulman
   Format: MarkdownItexThe movers are coming to our apartment at 8am tomorrow morning, but GoILS is actually available [online](http://www.math.uchicago.edu/~may/BOOKS/geom_iter.pdf) 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 14th 2010
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   Author: Todd_Trimble
   Format: MarkdownItexThanks! 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 $$\Omega |B(S, C_1, Y) | \simeq |B(\Omega S, C_1, Y)|$$ which I seem to recall May doing. My memory is that there is some hard topology here and there.

   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

   $$\Omega |B(S, C_1, Y) | \simeq |B(\Omega S, C_1, Y)|$$

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

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeJun 14th 2010
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   Author: Mike Shulman
   Format: MarkdownItexYes, I think your memory is right.

   Yes, I think your memory is right.