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

Keywords

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

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