Surgery formulas for Seiberg-Witten invariants and family Seiberg-Witten invariants

Haochen Qiu

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arXiv · 2411.10392

Surgery formulas for Seiberg-Witten invariants and family Seiberg-Witten invariants

Haochen Qiu

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Abstract

We prove a surgery formula for the ordinary Seiberg-Witten invariants, and surgery formulas for the families Seiberg-Witten invariants of families of $4$-manifolds obtained through fibrewise surgery. Our formula expresses the Seiberg-Witten invariants of the manifold after the surgery, in terms of the original Seiberg-Witten moduli space cut down by a cohomology class in the configuration space. We use these surgery formulas to study how a surgery can preserve or produce exotic phenomena.

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BibTeX RIS

Haochen Qiu. 2024-11-15. Surgery formulas for Seiberg-Witten invariants and family Seiberg-Witten invariants. https://arxiv.org/abs/2411.10392

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