${\mathrm{H}}^4({\mathrm{Co}}_0;\mathbf{Z})=\mathbf{Z}/24$

Theo Johnson-Freyd, David Treumann

We show that the fourth integral cohomology of Conway's group ${\mathrm{Co}}_0$ is a cyclic group of order $24$, generated by the first fractional Pontryagin class of the $24$-dimens…