|
Higher type adjunction inequalities for Donaldson invariants
Author(s):
Vicente
Muñoz
Journal:
Trans. Amer. Math. Soc.
353
(2001),
2635-2654.
MSC (2000):
Primary 57R57;
Secondary 57R58
Posted:
March 15, 2001
MathSciNet review:
1828464
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove new adjunction inequalities for embedded surfaces in four-manifolds with non-negative self-intersection number using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsváth and Szabó using the Seiberg-Witten invariants. To prove these relations, we give a fairly explicit description of the structure of the Fukaya-Floer homology of a surface times a circle. As an aside, we also relate the Floer homology of a surface times a circle with the cohomology of some symmetric products of the surface.
References:
-
- 1.
- A. Bertram and M. Thaddeus, On the quantum cohomology of a symmetric product of an algebraic curve, math.AG/9803026
- 2.
- S. Dostoglou and D. Salamon, Self-dual instantons and holomorphic curves, Annals of Math., 139 1994, 581-640. MR 95g:58050
- 3.
- R. Fintushel and R. J. Stern, The blow-up formula for Donaldson invariants, Annals of Math. 143 1996, 529-546. MR 97i:57036
- 4.
- K. Fukaya, Instanton homology for oriented
 -manifolds, Adv. Studies in Pure Mathematics, Ed. Y. Matsumoto and S. Morita. - 5.
- P. B. Kronheimer and T. S. Mrowka, Embedded surfaces and the structure of Donaldson's polynomial invariants, J. Diff. Geom. 41 1995, 573-734. MR 96e:57019
- 6.
- I. G. MacDonald, Symmetric products of an algebraic curve, Topology, 1 1962, 319-343. MR 27:1445
- 7.
- V. Muñoz, Gluing formulae for Donaldson invariants for connected sums along surfaces, Asian J. Math. 1 1997, 785-800. MR 99m:57027
- 8.
- V. Muñoz, Ring structure of the Floer cohomology of
 , Topology, 38 1999, 517-528. MR 99m:57028 - 9.
- V. Muñoz, Fukaya-Floer homology of
 and applications, to appear in J. Diff. Geom. - 10.
- V. Muñoz, Basic classes for four-manifolds not of simple type, Comm. Anal. Geom. 8 2000, 653-670. CMP 2000:16
- 11.
- V. Muñoz and B-L. Wang, Seiberg-Witten-Floer homology of a surface times a circle, math.DG/9905050.
- 12.
- P. Osváth and Z. Szabó, Higher type adjunction inequalities in Seiberg-Witten theory, math.DG/0005268.
- 13.
- E. Witten, Monopoles and four-manifolds, Math. Research Letters, 1 1994, 769-796. MR 96d:57035
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
57R57,
57R58
Retrieve articles in all Journals with
MSC (2000):
57R57,
57R58
Additional Information:
Vicente
Muñoz
Affiliation:
Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
Address at time of publication:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email:
vicente.munoz@uam.es
DOI:
10.1090/S0002-9947-01-02793-3
PII:
S 0002-9947(01)02793-3
Keywords:
4-manifolds,
adjunction inequalities,
Donaldson invariants,
Fukaya-Floer homology
Received by editor(s):
February 23, 1999
Posted:
March 15, 2001
Additional Notes:
Partially supported by DGES through Spanish Research Project PB97-1095
Copyright of article:
Copyright
2001,
American Mathematical Society
|
