To put my question in context, I'm reading Hatcher's book on Spectral sequences is which is say " The suspension homomorphism $E$ is the map on $pi_{i}$ induced by the natural inclusion map $S^{n}\rightarrow \Omega S^{n+1}$ adjoint to the identity $\Sigma S^{n} \rightarrow\Sigma S^{n}=S^{n+1}$."
2026-03-26 12:35:17.1774528517
What does the $\Omega$ represent in $\Omega S^{n}$?
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$\Omega X$ of a topological space X is the same as the loop space of X, see http://en.wikipedia.org/wiki/Loop_space for more info.