Home > Research > Publications & Outputs > Pseudoholomorphic tori in the Kodaira-Thurston ...

Research

Associated organisational unit

Electronic data

  • 1205.1239

    Accepted author manuscript, 387 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

Keywords

View graph of relations

Pseudoholomorphic tori in the Kodaira-Thurston manifold

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Pseudoholomorphic tori in the Kodaira-Thurston manifold. / Evans, Jonathan David; Kedra, Jarek.
In: Compositio Mathematica, Vol. 151, No. 12, 16.07.2015, p. 2212-2250.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Evans, JD & Kedra, J 2015, 'Pseudoholomorphic tori in the Kodaira-Thurston manifold', Compositio Mathematica, vol. 151, no. 12, pp. 2212-2250. https://doi.org/10.1112/S0010437X15007460

APA

Evans, J. D., & Kedra, J. (2015). Pseudoholomorphic tori in the Kodaira-Thurston manifold. Compositio Mathematica, 151(12), 2212-2250. https://doi.org/10.1112/S0010437X15007460

Vancouver

Evans JD, Kedra J. Pseudoholomorphic tori in the Kodaira-Thurston manifold. Compositio Mathematica. 2015 Jul 16;151(12):2212-2250. doi: 10.1112/S0010437X15007460

Author

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

Bibtex

@article{190685ee73a449b8ab5c703e066f5731,
title = "Pseudoholomorphic tori in the Kodaira-Thurston manifold",
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-K{\"a}hler manifold. ",
keywords = "family Gromov-Witten invariant, pseudoholomorphic curves, non-Kahler, Kodaira-Thurston, nilpotent Lie group",
author = "Evans, {Jonathan David} and Jarek Kedra",
year = "2015",
month = jul,
day = "16",
doi = "10.1112/S0010437X15007460",
language = "English",
volume = "151",
pages = "2212--2250",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "12",

}

RIS

TY - JOUR

T1 - Pseudoholomorphic tori in the Kodaira-Thurston manifold

AU - Evans, Jonathan David

AU - Kedra, Jarek

PY - 2015/7/16

Y1 - 2015/7/16

N2 - 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.

AB - 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.

KW - family Gromov-Witten invariant

KW - pseudoholomorphic curves

KW - non-Kahler

KW - Kodaira-Thurston

KW - nilpotent Lie group

U2 - 10.1112/S0010437X15007460

DO - 10.1112/S0010437X15007460

M3 - Journal article

VL - 151

SP - 2212

EP - 2250

JO - Compositio Mathematica

JF - Compositio Mathematica

SN - 0010-437X

IS - 12

ER -