Pseudoholomorphic tori in the Kodaira-Thurston manifold
arXiv:1205.1239 · doi:10.1112/S0010437X15007460
Abstract
The Kodaira-Thurston manifold is a quotient of a nilpotent Lie group by a cocompact lattice. We compute the family Gromov-Witten invariants which count pseudoholomorphic tori in the Kodaira-Thurston manifold. For a fixed symplectic form the Gromov-Witten invariant is trivial so we consider the twistor family of left-invariant symplectic forms which are orthogonal for some fixed metric on the Lie algebra. This family defines a loop in the space of symplectic forms. This is the first example of a genus one family Gromov-Witten computation for a non-Kähler manifold.
46 pages; v2 added some references and explanation, v3 couple of typos corrected. To appear in Compositio Mathematica