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  • 1205.1239

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Pseudoholomorphic tori in the Kodaira-Thurston manifold

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>16/07/2015
<mark>Journal</mark>Compositio Mathematica
Issue number12
Volume151
Number of pages39
Pages (from-to)2212-2250
Publication statusPublished
Original languageEnglish

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.