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Pseudoholomorphic tori in the Kodaira-Thurston manifold

Evans, JD; Kedra, J; (2012) Pseudoholomorphic tori in the Kodaira-Thurston manifold. [Digital scholarly resource]. http://arxiv.org/abs/1205.1239

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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.

Type: Digital scholarly resource
Title: Pseudoholomorphic tori in the Kodaira-Thurston manifold
Publisher version: http://arxiv.org/abs/1205.1239
Keywords: symplectic manifolds, Gromov-Witten theory
UCL classification: UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics
URI: http://discovery.ucl.ac.uk/id/eprint/1360031
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