On self-dual pseudo-connections on some orbifolds (Q1188012)

The author adapts the gauge theory developed by \textit{S. Donaldson} for definite 4-manifolds to the study of certain definite 4-dimensional orbifolds whose singularities are cones on lens spaces. As a corollary it is shown that if such an orbifold \(X\) has \(\pi_ i(X)=0\), \(H_ 2(X;Q)=0\), and at least one singularity that is the cone on a lens space \(L(p,1)\) with \(p\neq 4\), then there must be another singularity which is also the cone on \(-L(p,1)\). This in turn implies that if \(L(p,1)\#- L(p',q)\) smoothly embeds in the 4-sphere, then \(L(p',q)\) is diffeomorphic to \(L(p,1)\). Furthermore the author gives a nice proof of \textit{Kuga}'s theorem [Topology 23, 133-137 (1984; Zbl 0551.57019)] about smooth embeddings of \(S^ 2\) into \(S^ 2\times S^ 2\).