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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A vanishing theorem for Donaldson invariants


Author: Paolo Lisca
Journal: Proc. Amer. Math. Soc. 123 (1995), 607-613
MSC: Primary 57R55; Secondary 57N13, 58D29
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 $ SU(2)$-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: http://dx.doi.org/10.1090/S0002-9939-1995-1233978-5
PII: S 0002-9939(1995)1233978-5
Keywords: 4-manifolds, gauge theory, Donaldson invariants
Article copyright: © Copyright 1995 American Mathematical Society