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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 15th 2016
    • (edited Aug 15th 2016)

    I have created Sullivan model of free loop space with the formula and pointers to the literature.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 16th 2016
    • (edited Aug 16th 2016)

    There is a canonical S 1S^1-action on the free loop space. For Sullivan models ( (VsV,d X)(\wedge^\bullet (V \oplus s V, d_{\mathcal{L}X} ) such that d Xd_X is simple enough, then it is easy to guess a Sullivan model for the S 1S^1-homotopy quotient. Namely add a generator ω 2\omega_2 of degre 2 and then modify the differential on the unshifted generators by adding a term proportional to the corresponding shifted generator wedge ω 2\omega_2.

    Is there any published statement about Sullivan models for the homotopy quotients X/S 1\mathcal{L}X/S^1?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 16th 2016

    I have found a source for the proof of the Sullivan model for X/S 1\mathcal{L}X/S^1. It is theorem A in Vigué-Burghelea 85. I have added the statement here.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 16th 2016

    I have added an Examples-section The 4-sphere and twisted de Rham cohomology which spells out the Sullivan model for S 4//S 1\mathcal{L}S^4 // S^1 and makes an observation of how this relates to a kind of caloron correspondence.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2019

    added as a corollary the Sullivan model for based loop spaces (here) and, as an example, the Sullivan models for the iterated based loop spaces of spheres Ω kS n\Omega^k S^{n} for k<nk \lt n (here)

    diff, v27, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2019

    changed title, making it just “loop space” instead of “free loop space”

    diff, v27, current

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