Seiberg-Witten invariants, orbifolds, and circle actions

Baldridge, Scott

doi:10.1090/S0002-9947-02-03205-1

Seiberg-Witten invariants, orbifolds, and circle actions
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by Scott Jeremy Baldridge

Trans. Amer. Math. Soc. 355 (2003), 1669-1697

DOI: https://doi.org/10.1090/S0002-9947-02-03205-1

Published electronically: December 6, 2002

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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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