Symplectic calabi-Yau 6-manifolds

Anar Akhmedov

doi:10.1016/j.aim.2014.05.013

Symplectic calabi-Yau 6-manifolds

Anar Akhmedov

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this article, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our method, we also construct symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group Z. This paper also produces the first examples of simply connected and non-simply connected symplectic Calabi-Yau 6-manifolds with fundamental groups Zp×Zq, and Z×Zq for any p ≥ 1 and q ≥ 2 via co-isotropic Luttinger surgery.

Original language	English (US)
Pages (from-to)	115-125
Number of pages	11
Journal	Advances in Mathematics
Volume	262
DOIs	https://doi.org/10.1016/j.aim.2014.05.013
State	Published - Sep 10 2014

Bibliographical note

Funding Information:
The author is grateful to Tian-Jun Li for valuable discussions and for his kind encouragement. The author is thankful to Robert Gompf for making various suggestions which have helped him in improving this paper. The author is also very grateful to the referee for constructive comments and suggestions that helped to improve the manuscript. The author is supported by NSF grants FRG DMS-1065955 and DMS-1005741 .

Keywords

Calabi-Yau 6-manifolds
Co-isotropic luttinger surgery
Lefschetz fibration
Symplectic connected sum

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title = "Symplectic calabi-Yau 6-manifolds",

abstract = "In this article, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our method, we also construct symplectic non-K{\"a}hler Calabi-Yau 6-manifolds with fundamental group Z. This paper also produces the first examples of simply connected and non-simply connected symplectic Calabi-Yau 6-manifolds with fundamental groups Zp×Zq, and Z×Zq for any p ≥ 1 and q ≥ 2 via co-isotropic Luttinger surgery.",

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note = "Funding Information: The author is grateful to Tian-Jun Li for valuable discussions and for his kind encouragement. The author is thankful to Robert Gompf for making various suggestions which have helped him in improving this paper. The author is also very grateful to the referee for constructive comments and suggestions that helped to improve the manuscript. The author is supported by NSF grants FRG DMS-1065955 and DMS-1005741 .",

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N1 - Funding Information: The author is grateful to Tian-Jun Li for valuable discussions and for his kind encouragement. The author is thankful to Robert Gompf for making various suggestions which have helped him in improving this paper. The author is also very grateful to the referee for constructive comments and suggestions that helped to improve the manuscript. The author is supported by NSF grants FRG DMS-1065955 and DMS-1005741 .

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N2 - In this article, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our method, we also construct symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group Z. This paper also produces the first examples of simply connected and non-simply connected symplectic Calabi-Yau 6-manifolds with fundamental groups Zp×Zq, and Z×Zq for any p ≥ 1 and q ≥ 2 via co-isotropic Luttinger surgery.

AB - In this article, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our method, we also construct symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group Z. This paper also produces the first examples of simply connected and non-simply connected symplectic Calabi-Yau 6-manifolds with fundamental groups Zp×Zq, and Z×Zq for any p ≥ 1 and q ≥ 2 via co-isotropic Luttinger surgery.

KW - Calabi-Yau 6-manifolds

KW - Co-isotropic luttinger surgery

KW - Lefschetz fibration

KW - Symplectic connected sum

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Symplectic calabi-Yau 6-manifolds

Abstract

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Keywords

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