Seminar

A classical construction due to Paul Biran [Bir, BK] allows to lift a Lagrangian submanifold L from a Donaldson Y divisor to a Lagrangian L′ in an ambient symplectic manifold X. In [BK], it is shown that if the minimal Chern number of Y is greater than 1, then the count of Maslov index 2 holomorphic disks with boundary on the lifted Lagrangian L′ is equivalent to the similar count of disks with boundary on L plus one extra disk. We study this enumerative geometry problem in the case when the minimal Chern number of Y is 1. This reveals several new, previously unexplored connections it has with relative closed- string Gromov-Witten theory of the pair (X, Y ). We explore applications, in particular, we use that to distinguish (up to action of Symp(X)) lifts of previously known Lagrangians.