Higher type adjunction inequalities for Donaldson invariants
Author:
Vicente Muñoz
Journal:
Trans. Amer. Math. Soc. 353 (2001), 26352654
MSC (2000):
Primary 57R57; Secondary 57R58
Published electronically:
March 15, 2001
MathSciNet review:
1828464
Fulltext PDF Free Access
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Abstract: We prove new adjunction inequalities for embedded surfaces in fourmanifolds with nonnegative selfintersection number using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsváth and Szabó using the SeibergWitten invariants. To prove these relations, we give a fairly explicit description of the structure of the FukayaFloer 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:
http://dx.doi.org/10.1090/S0002994701027933
PII:
S 00029947(01)027933
Keywords:
4manifolds,
adjunction inequalities,
Donaldson invariants,
FukayaFloer homology
Received by editor(s):
February 23, 1999
Published electronically:
March 15, 2001
Additional Notes:
Partially supported by DGES through Spanish Research Project PB971095
Article copyright:
© Copyright 2001 American Mathematical Society
