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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Recurrence relations and asymptotics for four-manifold invariants
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by P. B. Kronheimer and T. S. Mrowka PDF
Bull. Amer. Math. Soc. 30 (1994), 215-221 Request permission


The polynomial invariants ${q_d}$ for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the polynomials. As an application, one can read off a lower bound for the genera of embedded surfaces from the asymptotics of ${q_d}$ for large d. The relations are proved using moduli spaces of singular instantons.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 30 (1994), 215-221
  • MSC (2000): Primary 57R55; Secondary 14J27, 14J29, 57N13, 57R40, 57R57
  • DOI:
  • MathSciNet review: 1246469