The based \(\text{SU}(n)\)-instanton moduli spaces
We give an \(L\)-stratification of \({\mathcal M}_ k\), the based moduli space of \(SU(n)\) instantons of charge \(k\) over \(S^ 4\). Then we prove that the stabilization map \(\iota_ k:{\mathcal M}_ k \to {\mathcal M}_{k+1}\) is an equivalence through a range \(q(k)\) which monotonically increases and tends to infinite as \(k \to \infty\). This proves the Atiyah-Jones conjecture for the group \(SU(n)\). As a by-product of the \(L\)- stratification we are able to conclude that \({\mathcal M}_ k\) are simply connected for all \(k\) and all \(n>2\).
scientific article; zbMATH DE number 537311