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Seiberg-Witten invariants, orbifolds, and circle actions

Author: Scott Jeremy Baldridge
Journal: Trans. Amer. Math. Soc. 355 (2003), 1669-1697
MSC (2000): Primary 57R57, 57M60; Secondary 55R35
Published electronically: December 6, 2002
MathSciNet review: 1946410
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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.

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Additional Information

Scott Jeremy Baldridge
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405

Keywords: Differential geometry, Seiberg-Witten invariants, circle actions, geometric topology
Received by editor(s): May 8, 2002
Received by editor(s) in revised form: September 6, 2002
Published electronically: December 6, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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