Pseudoholomorphic tori in the Kodaira-Thurson manifold

Jonathan David Evans, Jarek Kedra

Research output: Contribution to journalArticle

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 sowe 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.
Original languageEnglish
Pages (from-to)2212-2250
Number of pages39
JournalCompositio Mathematica
Volume151
Issue number12
Early online date16 Jul 2015
DOIs
Publication statusPublished - Dec 2015

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Symplectic Form
Torus
Gromov-Witten Invariants
Twistors
Nilpotent Lie Group
Lie Algebra
Genus
Count
Quotient
Trivial
Metric
Invariant
Family

Keywords

  • family Gromov–Witten invariant
  • pseudoholomorphic curve
  • non-Kähler
  • Kodaira–Thurston
  • nilpotent Lie group

Cite this

Pseudoholomorphic tori in the Kodaira-Thurson manifold. / Evans, Jonathan David; Kedra, Jarek.

In: Compositio Mathematica, Vol. 151, No. 12, 12.2015, p. 2212-2250.

Research output: Contribution to journalArticle

Evans, Jonathan David ; Kedra, Jarek. / Pseudoholomorphic tori in the Kodaira-Thurson manifold. In: Compositio Mathematica. 2015 ; Vol. 151, No. 12. pp. 2212-2250.
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