Seiberg-Witten invariants, orbifolds, and circle actions

Details Seiberg-Witten invariants, orbifolds, and circle actions Seiberg-Witten invariants, orbifolds, and circle actions

2001-07-12

arxiv.org/abs/math/0107092v1

Mathematics

Geometric Topology

Latex, 27 pages, 2 figures

Scientific paper

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 b_+>1 4-manifolds with fixed-point free circle actions are simple type and a new proof that the four dimensional invariants of $Y \times S^1$ are equal to the the three dimensional invariants of $Y$. An infinite number of b_+=1 4-manifolds where the Seiberg-Witten invariants are still diffeomorphism invariants are constructed and studied.

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