Pseudoholomorphic tori in the Kodaira-Thurston manifold
Symplectic Geometry
2015-12-23 v3 Algebraic Geometry
Differential Geometry
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-K\"ahler manifold.
Keywords
Cite
@article{arxiv.1205.1239,
title = {Pseudoholomorphic tori in the Kodaira-Thurston manifold},
author = {Jonathan David Evans and Jarek Kędra},
journal= {arXiv preprint arXiv:1205.1239},
year = {2015}
}
Comments
46 pages; v2 added some references and explanation, v3 couple of typos corrected. To appear in Compositio Mathematica