The Chow ring of the moduli space of bundles on \(\mathbb P^2\) with charge 1 (Q932935)

Principal \(\text{SO}(n)\)-bundles over \(S^4\) are classified by the ring of integers. The authors consider the principal bundle \(P_1\) and denote with \(M\) the space of equivalence classes of \(\text{SO}(n)\)-instantons on \(P_1\). For \(n\geq 5\), \(M\) is known to be diffeomorphic to \(OM\), the moduli space of holomorphic principal bundles on \(\mathbb P^2_\mathbb C\), suct that \(c_2=2\), and with a given trivialization over a fixed line \(\ell_\infty\). Using this characterization, the authors are able to determine the structure of the Chow ring of \(M\). The structure depends on the remainder of \(n\bmod 4\).