A vanishing theorem for Donaldson invariants

Author:
Paolo Lisca

Journal:
Proc. Amer. Math. Soc. **123** (1995), 607-613

MSC:
Primary 57R55; Secondary 57N13, 58D29

DOI:
https://doi.org/10.1090/S0002-9939-1995-1233978-5

MathSciNet review:
1233978

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Abstract: Given a smooth simply connected 4-manifold *M*, we prove that if there is a smoothly embedded 2-torus *T* inside *M*, then the -Donaldson invariants of *M* vanish on collections of 2-homology classes, all of which are orthogonal to [*T*] and at least two of which are multiples of [*T*]. From this we deduce obstructions to the representability of 2-homology classes of some algebraic surfaces by smoothly embedded tori, and we compute the group of self-diffeomorphisms of certain 4-manifolds with boundary.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1233978-5

Keywords:
4-manifolds,
gauge theory,
Donaldson invariants

Article copyright:
© Copyright 1995
American Mathematical Society