|
The geography of irreducible 4-manifolds
Author(s):
Jongil
Park
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2493-2503.
MSC (1991):
Primary 57N13, 57R55
MathSciNet review:
1487335
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we investigate the existence and the uniqueness problems for simply connected irreducible  -manifolds. By taking fiber sums along an embedded surface of square  and by a rational blow-down procedure, we construct many new irreducible  -manifolds which have infinitely many distinct smooth structures. Furthermore, we prove that all but at most finitely many lattice points lying in the non-positive signature region with  are covered by these irreducible  -manifolds.
References:
- [C]
- Z. Chen, On the geography of surfaces: Simply connected minimal surfaces with positive index, Math. Ann. 277, 141-164 (1987). MR 88c:14057
- [FS1]
- R. Fintushel and R. Stern, Surgery in cusp neighborhoods and the geography of irreducible 4-manifolds, Inventiones Math. 117, 455-523 (1994). MR 95f:57040
- [FS2]
- R. Fintushel and R. Stern, Rational blowdowns of smooth 4-manifolds, J. Diff. Geo., to appear.
- [G]
- R. Gompf, A new construction of symplectic manifolds, Annals of Math. 142, 527-595 (1995). MR 96j:57025
- [K]
- D. Kotschick, The Seiberg-Witten invariants of symplectic four-manifolds [after C.H. Taubes], Seminaire Bourbaki. 48eme annee, no 812 (1995-96), Astérisque, no. 241, Soc. Math. France, Paris, 1997, pp. 195-220. CMP 98:01
- [L]
- W. Lorek, private communication.
- [MMS]
- J. Morgan, T. Mrowka and Z. Szabó, Product formulas along
 for Seiberg-Witten invariants, in preparation. - [MST]
- J. Morgan, Z. Szabó and C. Taubes, A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture, J. Diff. Geo. 44, 706-788 (1996). MR 97m:57052
- [P]
- U. Persson, An introduction to the geography of surfaces of general type, Proc. Symp. Pure Math. vol 46, 195-217 (1987). MR 89a:14057
- [S]
- A. Stipsicz, A note on the geography of symplectic manifolds, Turkish J. Math. 20 no 1, 135-139 (1996). MR 97m:57035
- [T]
- C. Taubes, The Seiberg-Witten and the Gromov invariants, Mathematical Research Letters 2, 221-238 (1995). MR 96a:57076
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
57N13, 57R55
Retrieve articles in all Journals with
MSC (1991):
57N13, 57R55
Additional Information:
Jongil
Park
Affiliation:
Department of Mathematics, University of California Irvine, Irvine, California 92697-3875
Address at time of publication:
Department of Mathematics, Kon-Kuk University, Kwangjin-gu Mojin-dong 93-1, Seoul 143-701, Korea
Email:
jpark@math.uci.edu, jipark@kkucc.konkuk.ac.kr
DOI:
10.1090/S0002-9939-98-04762-5
PII:
S 0002-9939(98)04762-5
Keywords:
Fiber sum,
irreducible manifold,
rational blow-down
Received by editor(s):
January 23, 1997
Communicated by:
Leslie Saper
Copyright of article:
Copyright
1998,
American Mathematical Society
|
