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Basic classes for four-manifolds not of simple type

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Publication Date
2000
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International Press
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We extend the notion of basic classes (for the Donaldson invariants) to 4-manifolds with b+ > 1 which are (potentially) not of simple type or satisfy b1 > 0.We also give a structure theorem for the Donaldson invariants of 4-manifolds with b+ > 1, b1 > 0 and of strong simple type.
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R. Fintushel and R. J. Stern, Donaldson invariants of 4-manifolds with simple type, Jour. Diff.Geometry, 42 1995, 577-633. R. Fintushel and R. J. Stern, The blow-up formula for Donaldson invariants, Annals of Math.143 1996, 529-546. P. B. Kronheimer and T. S. Mrowka, Embedded surfaces and the structure of Donaldson’s polynomial invariants, Jour. Differential Geometry, 41 1995, 573-734. P. B. Kronheimer and T. S. Mrowka, The structure of Donaldson’s invariants for four-manifolds not of simple type, http://www.math.harvard.edu/HTML/Individuals/Peter Kronheimer.html V. Muñoz, Fukaya-Floer homology of × S1 and applications, math.DG/9804081. A. Stipsicz, Ph. D. Thesis, Rutgers University, NJ,Computations of Donaldson invariants viacut and paste techniques, 1994.
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