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

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

Published electronically:
December 6, 2002

MathSciNet review:
1946410

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Abstract | References | Similar Articles | Additional Information

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 -manifolds with fixed-point-free circle actions are simple type and a new proof of the equality . An infinite number of -manifolds with 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

Email:
sbaldrid@indiana.edu

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

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