Homology of the $MSU$ Spectrum

Semyon A. Abramyan

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Tome 318 (2022), pp. 5-16

Résumé

We give a complete proof of the Novikov isomorphism $\varOmega ^{{SU}}\otimes \mathbb Z \bigl [\tfrac 12\bigr ]\cong \mathbb Z\bigl [\tfrac 12\bigr ] [y_2,y_3,\ldots ]$, $\deg y_i=2i$, where $\varOmega ^{{SU}}$ is the ${SU}$-bordism ring. The proof uses the Adams spectral sequence and a description of the comodule structure of $H_{\scriptscriptstyle\bullet}({M\kern -1pt SU};\mathbb F_p)$ over the dual Steenrod algebra $\mathfrak A_p^*$ with odd prime $p$, which was also missing in the literature.