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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.

3 votes

Geometric realization of Hochschild complex

Sam Gunningham had the right idea, but I would like to fix it up for the construction of the homotopy pullback that I am aware of. Alternatively one can compute $HH(A;A)$ as $\mathrm{Tor}^{A^e}(A,A)$ …
Justin Noel's user avatar
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