A surgery formula for Seiberg-Witten invariants

Haochen Qiu

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arXiv · 2409.02265

A surgery formula for Seiberg-Witten invariants

Haochen Qiu

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Abstract

We prove a surgery formula for the ordinary Seiberg-Witten invariants of smooth $4$-manifolds with $b_1 =1$. 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. This formula can be used to find exotic smooth structures on nonsimply connected $4$-manifolds, and gives a lower bound of the genus of an embedding surface in nonsimply connected $4$-manifolds. In forthcoming work, we will extend these results to give a surgery formula for the families Seiberg-Witten invariants.

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Haochen Qiu. 2024-09-03. A surgery formula for Seiberg-Witten invariants. https://arxiv.org/abs/2409.02265

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