Loop-space homology ($H_{\ast }(\Omega X)$)

Loop-space homology is the homology of the based loop space. It also carries the Pontryagin product induced by concatenation of loops. For $n>2$, a Morse theory cell structure on $\Omega S^n$ has one cell in each dimension $j(n-1)$, so its integer homology is $\mathbb{Z}$ in those dimensions and zero elsewhere.