Lie Groups Seminar
The finite-dimensional equivariant moduli problmes arise from the study of the moduli spaces of J-holomorphic curves and the study of invariants of Hamiltonian group actions. From the stratification theory point of view, we show that there exists a stratified obstruction system for an equivariant moduli problem. In addition, we introduce a coindex for a G-vector bundle that is determined by the G-action on the vector bundle. We show that if the coindex of an oriented equivariant moduli problem is bigger than 1, then we obtain an invariant Euler cycle via a smooth equivariant perturbation. This talk is based on my thesis completed in Sichuan University.