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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 23rd 2012

    started an entry on the Borel construction, indicating its relation to the nerve of the action groupoid.

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeMar 23rd 2012
    • (edited Mar 23rd 2012)

    That is very useful and very ’timely’ as I was looking for a good reference for the Borel construction and orbifolds. :-)

    • CommentRowNumber3.
    • CommentAuthorjim_stasheff
    • CommentTimeMar 23rd 2012
    I've done a very slight edit including the alternate name homotopy quotient but that leads to something in which homotopy quotient appears only very weakly.
    • CommentRowNumber4.
    • CommentAuthorMatanP
    • CommentTimeMar 23rd 2012

    added a subsection called

    As a homotopy colimit over the category associated to GG

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 21st 2020
    • (edited Oct 21st 2020)

    This entry was lacking a decent reference. I have taken the liberty now of pointing to

    Please feel invited to add you favorite classical textbook account on the Borel construction, instead (which is?)

    diff, v11, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 4th 2021
    • (edited Jul 4th 2021)

    added mentioning of the simplicial version and some lines (here) relating to the model structure on simplicial group actions

    diff, v13, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 14th 2021

    I have written out a proof (here) that the topological Borel construction of a well-pointed topological group action sits in the evident homotopy fiber sequence

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 17th 2021

    I have added statement and proof (here) that the topological Borel construction of a free action is weakly equivalent – under some sufficient conditions – to the plain quotient.

    diff, v17, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2021

    have removed, in that Prop, the assumption that the fundamental group is abelian, and instead added the remark to the proof that the five-lemma still applies.

    Of course it does. I have tried to make up for being silly here, previously, by expanding a little at five lemma on the case of homological categories.

    diff, v19, current