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Results tagged with loop-spaces
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user 148988
The loop space $Ω_X$ of a pointed topological space $X$ is the space of based maps from the circle $\mathbb S^1$ to $X$ with the compact-open topology.
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If $\Omega X \simeq \Omega Y$ then is $X \simeq Y$ for $X,Y$ simply connected?
If $\Omega X \simeq \Omega Y$ then is $X \simeq Y$ for $X,Y$ simply connected?
Assuming $X,Y$ are nice spaces like CW of course.
Clearly this is true by Whitehead, but I am looking for a more enligh …
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