SYMPLECTIC GEOGRAPHY PROBLEM IN DIMENSION SIX

Year 2012, Volume: 41 Issue: 5, 709 - 713, 01.05.2012

Ahmet Beyaz

https://izlik.org/JA93NB94YL

Abstract

SYMPLECTIC GEOGRAPHY PROBLEM IN DIMENSION SIX

https://izlik.org/JA93NB94YL

Abstract

In this note, the geography problem in dimension four is reviewed and then its extension to dimension six for the symplectic case is explained. Finally some examples in dimension six are provided.

Keywords

Symplectic , 6-manifold , 4-manifold , Geography

References

• Akhmedov, A. Simply Connected Symplectic Calabi-Yau 6-Manifolds, Arxiv preprint arXiv:1107.2623, 2011.
• Fintushel, R. and Stern, R. J. Knots, links, and 4-manifolds, Invent. Math. 134 (2), 363–400, 1998.
• Fintushel, R. and Stern, R. J. Families of simply connected 4-manifolds with the same Seiberg-Witten invariants, Topology 43 (6), 1449–1467, 2004.
• Fintushel, R. and Stern, R. J. Six lectures on four 4-manifolds (Low Dimensional Topology, IAS/Park City Math. Ser. 15, Amer. Math. Soc., Providence, RI, 2009), 265–315.
• Gompf, R. E. A new construction of symplectic manifolds, Ann. of Math. (2) 142 (3), 527– 595, 1995.
• Gompf, R. E. and Stipsicz, A. I. 4-manifolds and Kirby calculus (Graduate Studies in Math- ematics 20, American Mathematical Society, Providence, RI, 1999).
• Halic, M. On the geography of symplectic 6-manifolds, Manuscripta Math. 99 (3), 371–381, 1999.
• Hunt, B. Complex manifold geography in dimension 2 and 3, J. Differential Geom.30 (1), 51–153, 1989.
• LeBrun, C. Topology versus Chern numbers for complex 3-folds, Pacific J. Math. 191 (1), 123–131, 1999.
• Okonek, Ch. and Van de Ven, A. Cubic forms and complex 3-folds, Enseign. Math. (2) 41(3-4), 297–333,1995.
• Weinstein, A. Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6, 329–346, 1971.