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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A vanishing theorem for Donaldson invariants
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by Paolo Lisca PDF
Proc. Amer. Math. Soc. 123 (1995), 607-613 Request permission

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
  • © Copyright 1995 American Mathematical Society
  • 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