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The based \(\text{SU}(n)\)-instanton moduli spaces. (English) Zbl 0788.32013
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 \(n>2\).

MSC:
32G13 Complex-analytic moduli problems
81T13 Yang-Mills and other gauge theories in quantum field theory
55P35 Loop spaces
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