Pseudoholomorphic tori in the Kodaira-Thurston manifold (Q2786460)

The Kodaira-Thurston manifold is a quotient of a nilpotent Lie group by a cocompact lattice. It is a real four-dimensional non-Kähler manifold. This paper computes the family of Gromov-Witten invariants which count the pseudoholomorphic tori in the Kodaira-Thurston manifold. For a fixed symplectic form, the Gromov-Witten invariant is trivial, so the authors consider the twistor family of left-invariant symplectic forms which are orthogonal for some fixed metric on the Lie algebra. This family corresponds to a loop in the space of symplectic forms. This is the first example of computation of genius-one family Gromov-Witten invariants of a non-Kähler manifold.