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

TL;DR

This paper proves that the fourth integral cohomology group of Conway's group Co0 is cyclic of order 24, generated by a specific characteristic class related to its 24-dimensional representation.

Contribution

It establishes the exact structure of the fourth integral cohomology of Co0 and identifies its generator as a fractional Pontryagin class.

Findings

H^4(Co0;Z) is cyclic of order 24

Generated by the first fractional Pontryagin class

Provides explicit cohomological characterization of Co0

Abstract

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 $24$-dimensional representation.