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 language | English |
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Pages (from-to) | 2212-2250 |
Number of pages | 39 |
Journal | Compositio Mathematica |
Volume | 151 |
Issue number | 12 |
Early online date | 16 Jul 2015 |
DOIs | |
Publication status | Published - Dec 2015 |
Keywords
- family Gromov–Witten invariant
- pseudoholomorphic curve
- non-Kähler
- Kodaira–Thurston
- nilpotent Lie group
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Jarek Kedra
- School of Natural & Computing Sciences, Mathematical Science - Personal Chair
Person: Academic