Transversality for multiply covered J-holomorphic curves

Jeudi 9 avril 2015 14:00-15:00 - Chris Wendl - UC London

Résumé : The Gromov-Witten invariants of symplectic manifolds are defined in principle by counting J-holomorphic curves for a generic tame almost complex structure. In practice, this definition is beset with well-known technical difficulties because multiply covered curves cannot be made regular just by choosing J generically, so transversality typically requires fancier methods such as multivalued perturbations or stabilizing divisors. In this talk, I will describe some situations in which the more naive approach actually works : in particular, the Gromov-Witten invariants of symplectic 4-manifolds can always be computed by counting honest J-holomorphic curves with no abstract or domain-dependent perturbations, leading to integrality results that are not apparent from more abstract definitions. The main technical hurdle is to prove transversality for rigid unbranched multiple covers, and for this we use an analytic perturbation technique originally introduced by Taubes. (This is joint work with Chris Gerig.)

Lieu : bât. 425 - 121-123

Transversality for multiply covered J-holomorphic curves  Version PDF