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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
Published electronically: March 15, 2001
MathSciNet review: 1828464
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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

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