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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 14th 2017

    I need a word for the homotopy quotient (X)/S 1(\mathcal{L}X)/S^1 of free loop spaces X\mathcal{L}X by their canonical circle action. It seems that the only term in use with respect to this is “twisted loop space”, which however usually refers just to the constant loops ( constX)//S 1(\mathcal{L}_{const}X)//S^1. Since under nice conditions the derived functions on the Spec(A)/S 1\mathcal{L}Spec(A)/S^1 is the cyclic homology complex of AA, I suggest that a good name is “cyclic loop space”. I made a quick note at cyclic loop space, just to fix and disambiguate terminology.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 21st 2021
    • (edited Jun 21st 2021)

    I have added pointer to cylic loop orbifolds in

    Also added pointer to our

    and

    from which some of the entry material had been taken.

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2021

    added pointer to:

    diff, v11, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2021

    also:

    diff, v11, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2021

    also:

    diff, v11, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2021
    • (edited Jul 2nd 2021)

    added (here) statement of the stable splitting theorem by Carlsson & Cohen 1987:

    Ω Σ (Maps(S 1,ΣX)S 1)(Ω Σ BS 1)×k 1Ω Σ ((E(/k)) + /kX n) \Omega^\infty \Sigma^\infty \big( Maps(S^1, \Sigma X) \sslash S^1 \big) \;\; \simeq \;\; \big( \Omega^\infty \Sigma^\infty B S^1 \big) \times \underset{ k \in \mathbb{N}_{\geq 1} }{\prod} \Omega^\infty \Sigma^\infty \big( (E (\mathbb{Z}/k))_+ \wedge_{\mathbb{Z}/k} X^{\wedge^n} \big)

    diff, v12, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2021

    also pointer to

    where this result was announced

    diff, v12, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeAug 18th 2021

    added pointer to:

    for the terminology “string space” (Section 4.8.1)

    diff, v13, current

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