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Family Seiberg-Witten invariants and wall crossing formulas

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arxiv math/0107211 v2 pith:RBHPYW7P submitted 2001-07-29 math.GT math.SG

Tian-Jun Li , Ai-Ko Liu This is my paper · ORCID
classification math.GTmath.SG
keywords familyseiberg-wittenchambercrossingformulasinvariantstheorywall
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In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber structure plays a more prominent role. We derive some wall crossing formulas measuring how the family Seiberg-Witten invariants change from one chamber to another.

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  1. Family Seiberg-Witten equation on Kahler surface and $\pi_i(\Symp)$ on multiple-point blow ups of Calabi-Yau surfaces

    math.GT 2024-12 reject novelty 6.0 of 10

    Infinite generation of some higher homotopy groups of symplectomorphism groups is proved for n-point Kahler blowups of tori, K3 surfaces, and Enriques surfaces with non-resonant Kahler classes.

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