HIGHER JET EVALUATION TRANSVERSALITY OF J-HOLOMORPHIC CURVES Yong-Geun Oh

Abstract. In this paper, we establish general stratawise higher jet evalu-ation transversality of J-holomorphic curves for a generic choice of almost complex structures J (tame to a given symplectic manifold (M;!)). Using this transversality result, we prove that there exists a subset J ram! J! of second category such that for every J 2 J ram! , the dimen-sion of the moduli space of (somewhere injective) J-holomorphic curves with a given ramication prole goes down by 2n or 2(n 1) depending on whether the ramication degree goes up by one or a new ramication point is created. We also derive that for each J 2 J ram! there are only a nite number of ramication proles of J-holomorphic curves in a given homology class 2 H2(M;Z) and provide an explicit upper bound on the number of rami cation proles in terms of c1 () and the genus g of the domain surface. Content