Evans, Jonathan David and Kedra, Jarek (2015) Pseudoholomorphic tori in the Kodaira-Thurston manifold. Compositio Mathematica, 151 (12). pp. 2212-2250. ISSN 0010-437X
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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.