Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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