Pseudoholomorphic tori in the Kodaira-Thurston manifold

Evans, Jonathan David and Kedra, Jarek (2015) Pseudoholomorphic tori in the Kodaira-Thurston manifold. Compositio Mathematica, 151 (12). pp. 2212-2250. ISSN 0010-437X

[img]
Preview
PDF (1205.1239)
1205.1239.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (395kB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Compositio Mathematica
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2602
Subjects:
ID Code:
132434
Deposited By:
Deposited On:
02 Apr 2019 10:55
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Mar 2020 06:29