A NOTE ON INDECOMPOSABLE 4-MANIFOLDS

Title & Authors
A NOTE ON INDECOMPOSABLE 4-MANIFOLDS
Cho, Yong-Seung; Hong, Yoon-Hi;

Abstract
In this note we show that there is an anti-symplectic involution $\small{\sigma\;:\;X\;\to\;X}$ on a simply-connected, closed, non-Kahler and symplectic 4-manifold X with a disjoint union of Riemann surfaces ${\amalg}^n_{i Keywords non-Kahler symplectic 4-manifold;anti-symplectic involution;Dolgachev surface;Seiberg-Witten invariant; Language English Cited by References 1. S. Akbulut, On quotients of complex surfaces under complex conjugation, J. Reine. Angew. Math. 447 (1994), 83-90 2. G. E. Bredon, Introduction to compact transformation groups, Academic Press, New York and London, 1972 3. Y. S. Cho, Cyclic group actions on gauge theory, Diffential. Geom. Appl. 6 (1996), 87-99 4. Y. S. Cho and Y. H. Hong, Cyclic group actions on 4-manifold, Acta. Math. Hungar. 94 (2002), no. 4, 333-350 5. Y. S. Cho and Y. H. Hong, Seiberg-Witten theory and anti-symplectic involutions, Glasg. Math. J. 45 (2003), 401-413 6. Y. S. Cho and Y. H. Hong, Anti-symplectic involutions on non-Kahler symplectic 4-manifolds, Preprint 7. M. Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982), 357-454 8. R. E. Gompf, A new construction of symplectic manifolds, Ann. of Math. 142 (1995), 527-595 9. R. E. Gompf and T. S. Mrowka, Irreducible 4-manifolds need not be complex, Ann. of Math. 138 (1993), 61-111 10. R. E. Gompf and A. I. Stipsciz, 4-Manifolds and Kirby Calculus, Grad. Stud. Math. 11. R. Kirby, Problems in low-dimensional topology, Berkeley, 1995 12. P. B. Kronheimer and T. S. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994), 797-808 13. J. W. Morgan, T. S. Mrowka, and Z. Szabo, Product formulas along$T^3\$ for Seiberg-Witten invariants, Math. Res. Lett. 4 (1997), 915-929

14.
J. W. Morgan, Z. Szabo, and C. Taubes, A product formula for the Seiberg- Witten invariants and the generalized Thom Conjecture, J. Differential Geom. 44 (1996), 706-788

15.
B. Ozbagci and A. I. Stipsciz, Non complex smooth 4-manifolds with genus 2- Lefschetz fibration

16.
A. I. Stipsciz, Manifolds not containing Gomph nuclei, Acta Math. 83 (1998), 107-113

17.
W. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), 467-468

18.
C. H. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994), 809-822

19.
C. H. Taubes, The Seiberg-Witten invariants and the Gromov invariants, Math. Res. Lett. 2 (1995), 221-238

20.
S. Wang, Gauge theory and involutions, Oxford University Thesis, 1990

21.
S. Wang, A Vanishing theorem for Seiberg-Witten invariants, Math. Res. Lett. 2 (1995), 305-310