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http://dx.doi.org/10.4134/JKMS.2007.44.4.757

ANTI-SYMPLECTIC INVOLUTIONS ON NON-KÄHLER SYMPLECTIC 4-MANIFOLDS  

Cho, Yong-Seung (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES, DEPARTMENT OF MATHEMATICS EWHA WOMANS UNIVERSITY)
Hong, Yoon-Hi (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 757-766 More about this Journal
Abstract
In this note we construct an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold which is constructed by Thurston and show that the quotient of the Thurston's 4-manifold is not symplectic. Also we construct a non-$K\ddot{a}hler$, symplectic 4-manifold using the Gomph's symplectic sum method and an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold.
Keywords
non-Kahler symplectic 4-manifold; anti-symplectic involution; Dolgachev surface; quotient manifold;
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1 S. Akbulut, On quotients of complex surfaces under complex conjugation, J. Reine. Angew. Math. 447 (1994), 83-90
2 W. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), no. 2, 467-468   DOI   ScienceOn
3 W. Barth, C. Peters, and A. Van de Ven, Compact Complex Surfaces, Springer, Heidelberg, 1984
4 Y. S. Cho, Cyclic group actions on gauge theory, Diff. Geom. and its Applications 6 (1996), no. 1, 87-99   DOI   ScienceOn
5 Y. S. Cho and Y. H. Hong, Cyclic group actions on 4-manifold, Acta. Math. Hung. 94 (2002), no. 4, 333-350   DOI
6 Y. S. Cho and Y. H. Hong, Seiberg-Witten invariants and (anti-)symplectic involutions, Glasg. Math. J. 45 (2003), no. 3, 401-413   DOI   ScienceOn
7 R. E. Gompf, A new construction of symplectic manifolds, Ann. of Math. (2) 142 (1995), no. 3, 527-595   DOI
8 R. E. Gompf and T. S. Mrowka, Irreducible 4-manifolds need not be complex, Ann. of Math. (2) 138 (1993), no. 1, 61-111   DOI
9 P. Shanahan, The Atiyah-Singer index theorem, An introduction. Lecture Notes in Mathematics, 638. Springer, Berlin, 1978
10 A. I. Stipsciz, Manifolds not containing Gomph nuclei, Acta Math. 83 (1998), 107-113   DOI
11 S. Wang, Gauge theory and involutions, Oxford University Thesis (1990)
12 R. E. Gompf and A. I. Stipsciz, 4-manifolds and Kirby calculus, Graduate Studies in Mathematics, 20. American Mathematical Society, Providence, RI, 1999
13 R. Kirby, Problems in low-dimensional topology, Edited by Rob Kirby. AMS/IP Stud. Adv. Math., 2.2, Geometric topology (Athens, GA, 1993), 35-473, Amer. Math. Soc., Providence, RI, 1997
14 D. Mcduff, Examples of simply-connected symplectic non-Kahlerian manifolds, J. Differential Geom. 20 (1984), no. 1, 267-277   DOI
15 B. Ozbagci and A. I. Stipsciz, Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations, Proc. Amer. Math. Soc. 128 (2000), no. 10, 3125-3128   DOI   ScienceOn
16 D. Salamon, Spin geometry and Seiberg-Witten invariants, University of Warwick, October 2, 1995