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Question A: The free loop space of a manifold is also a manifold?

Question B: The free loop space of an algebraic variety is also a algebraic variety ?

Are these questions asked or answered anywhere else? Any comments or references are welcomed.

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A: Yes. See this article in Wikipedia.

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  • $\begingroup$ Thanks, Let now $X$ a compact manifold and $p: X^{S^1}\longrightarrow X$ a fibration that admits sections. Set $Sect(p)$ the non empty set of that sections, topologized with the open compact topology. My question is: $Sect(p)$ inherits also a structure of manifold $\endgroup$
    – MyIsmail
    May 13, 2015 at 13:25