Higher type adjunction inequalities for Donaldson invariants

Author:
Vicente Muñoz

Journal:
Trans. Amer. Math. Soc. **353** (2001), 2635-2654

MSC (2000):
Primary 57R57; Secondary 57R58

DOI:
https://doi.org/10.1090/S0002-9947-01-02793-3

Published electronically:
March 15, 2001

MathSciNet review:
1828464

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Abstract | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0002-9947-01-02793-3

Keywords:
4-manifolds,
adjunction inequalities,
Donaldson invariants,
Fukaya-Floer homology

Received by editor(s):
February 23, 1999

Published electronically:
March 15, 2001

Additional Notes:
Partially supported by DGES through Spanish Research Project PB97-1095

Article copyright:
© Copyright 2001
American Mathematical Society