Perversity equals weight for Painlevé spaces

We provide further evidence to the P = W conjecture of de Cataldo, Hausel and Migliorini, by checking it in Painlevé cases. Namely, we compare perverse Leray filtration induced Hitchin map on cohomology spaces Dolbeault moduli space weight irregular character variety corresponding each I ? V systems. find that two filtrations agree. Along way, prove Geometric Katzarkov, Noll, Pandit Simpson cases, show these cases implies conjecture.