Homology of the completion of instanton moduli spaces (Q1420683)

Let \(M(k,G)\) be the moduli space of based gauge equivalence classes of G-instantons on \(S^{4}\) with instanton number \(k\). \(M(k,G)\) has the Uhlenbeck completion \(\overline{M}(k,G)= \bigcup _{q=0}^{k} SP^{q}(\mathbb{R} ^{4})\times M(k-q,G),\) where \(SP^{q}(\mathbb{R}^{4})\) denotes the \(q\)-fold symmetric product of \(\mathbb{R}^{4}.\) Let \(X(k,G)\) be the first two strata of the completion: \(X(k,G)=M(k,G)\cup \mathbb{R}^{4}\times M(k-1,G).\) The paper studies the homology of \(X(k,G)\) for \(G=SU(n)\) or \(Sp(n)\) and relates this cohomology to homology of a certain homotopy-theoretic fibre.