Bubble tree compactification and Kotschick-Morgan conjecture

Given a SU(2) or SO(3) principal bundle over an oriented compact Riemannian 4-manifold, the solutions to Yang-Mills equation give a space of anti-self-dual (ASD) connections. After quotienting the gauge transformation group, we have the instanton moduli space. In general the moduli space is non-compact. A well-known compactification is the Uhlenbeck compactification. But the lower strata in Uhlenbeck compactification lacks smoothness. Following the work of Bohui Chen I will explain the bubble tree compactification, which gives us a smooth orbifold structure on the instanton moduli space. This new compactification can be applied to prove the Kotschick-Morgan conjecture.