How concretely can the (based) loop space $\Omega S^1$ of $S^1$ be described? I know it's a space with homotopy groups $\pi_0(\Omega S^1) \simeq \mathbb{Z}$ and $\pi_i(\Omega S^1) \simeq 0$ for $i>0$, so $\Omega S^1$ has countably infinite components, each of which is contractible. What else can one say about it?
2026-04-22 11:19:06.1776856746
Loop space of $S^1$
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