Seifert fibered four-manifolds with nonzero Seiberg-Witten invariant

Weimin Chen

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arXiv · 1103.5681

Seifert fibered four-manifolds with nonzero Seiberg-Witten invariant

Weimin Chen

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Abstract

The main result of this paper asserts that if a Seifert fibered 4-manifold has nonzero Seiberg-Witten invariant, the homotopy class of regular fibers has infinite order. This is a nontrivial obstruction to smooth circle actions; as applications, we show how to destroy smooth circle actions on a 4-manifold by knot surgery, without changing the integral homology, intersection form, and even the Seiberg-Witten invariant. Results concerning classification of Seifert fibered complex surfaces or symplectic 4-manifolds are included. We also show that every smooth circle action on the 4-torus is smoothly conjugate to a linear action.

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BibTeX RIS

Weimin Chen. 2011-12-06. Seifert fibered four-manifolds with nonzero Seiberg-Witten invariant. https://arxiv.org/abs/1103.5681

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