On homology of the $MSU$ spectrum

Abstract

We give a complete proof the Novikov isomorphism ${\Omega }^{SU}\otimes \mathbb{Z}[\frac{1}{2}]\cong \mathbb{Z}[\frac{1}{2}][y_2,y_3,\dots ],\mathrm{deg}{y}_i=2i$, where ${\Omega }^{SU}$ is the $SU$-bordism ring. The proof uses the Adams spectral sequence and a description of the comodule structure of $H_{\ast }(MSU;{\mathbb{F}}_p)$ over the dual Steenrod algebra ${\mathfrak{A}}_p^{\ast }$ with odd prime $p$, which was also missing in the literature.