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In the study of moduli spaces defined by the anti-self-dual (ASD) Yang-Millsequations on $SU(2)$ or $SO(3)$ bundles over closed oriented Riemannian4-manifolds $M$, the bubble tree compactification was defined in [T88], [F95],[C02], [C10], [F14] and [F15]. The smooth orbifold structure of the bubble treecompactification away from the trivial stratum is defined in [C02] and [C10].In this paper, we apply the technique to 4-orbifolds of the form $M/\mathbbZ_\alpha$ satisfying Condition \ref{the assumption of group action in thisthesis} to get a bubble tree compactification of the instanton moduli space onthis particular kind of 4-orbifolds.

Bubble tree compactification of instanton moduli spaces on 4-orbifolds