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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 14th 2017

I need a word for the homotopy quotient $(\mathcal{L}X)/S^1$ of free loop spaces $\mathcal{L}X$ 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 $(\mathcal{L}_{const}X)//S^1$. Since under nice conditions the derived functions on the $\mathcal{L}Spec(A)/S^1$ is the cyclic homology complex of $A$, 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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJul 2nd 2021

added pointer to:

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 2nd 2021

also:

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJul 2nd 2021

also:

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

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

$\Omega^\infty \Sigma^\infty \big( Maps(S^1, \Sigma X) \sslash S^1 \big) \;\; \simeq \;\; \big( \Omega^\infty \Sigma^\infty B S^1 \big) \times \underset{ k \in \mathbb{N}_{\geq 1} }{\prod} \Omega^\infty \Sigma^\infty \big( (E (\mathbb{Z}/k))_+ \wedge_{\mathbb{Z}/k} X^{\wedge^n} \big)$
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 2nd 2021

also pointer to

where this result was announced

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeAug 18th 2021

added pointer to:

for the terminology “string space” (Section 4.8.1)

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