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

3 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

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.",

keywords = "Calabi-Yau 6-manifolds, Co-isotropic luttinger surgery, Lefschetz fibration, Symplectic connected sum",

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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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