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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Seiberg-Witten invariants, orbifolds, and circle actions
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by Scott Jeremy Baldridge PDF
Trans. Amer. Math. Soc. 355 (2003), 1669-1697 Request permission

Abstract:

The main result of this paper is a formula for calculating the Seiberg-Witten invariants of 4-manifolds with fixed-point-free circle actions. This is done by showing under suitable conditions the existence of a diffeomorphism between the moduli space of the 4-manifold and the moduli space of the quotient 3-orbifold. Two corollaries include the fact that $b_+ {>} 1$ $4$-manifolds with fixed-point-free circle actions are simple type and a new proof of the equality $\mathcal {SW}_{Y^3\times S^1} = \mathcal {SW}_{Y^3}$. An infinite number of $4$-manifolds with $b_+=1$ whose Seiberg-Witten invariants are still diffeomorphism invariants is constructed and studied.
References
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Additional Information
  • Scott Jeremy Baldridge
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
  • Email: sbaldrid@indiana.edu
  • Received by editor(s): May 8, 2002
  • Received by editor(s) in revised form: September 6, 2002
  • Published electronically: December 6, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 1669-1697
  • MSC (2000): Primary 57R57, 57M60; Secondary 55R35
  • DOI: https://doi.org/10.1090/S0002-9947-02-03205-1
  • MathSciNet review: 1946410