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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2412.19375 |
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| _version_ | 1866909675318935552 |
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| author | Du, Yi |
| author_facet | Du, Yi |
| contents | Let $ω$ be a Kahler form on $M$, which is a torus $T^4$, a $K3$ surface or an Enriques surface, let $M\#n\overline{\mathbb{CP}^2}$ be $n-$point Kahler blowup of $M$. Suppose that $κ=[ω]$ satisfies certain irrationality condition. Applying techniques related to deformation of complex objects, we extend the guage-theoretic invariant on closed Kahler suraces developed by Kronheimer\cite{Kronheimer1998} and Smirnov\cite{Smirnov2022}\cite{Smirnov2023}. As a result, we show that even dimensional higher homotopy groups of $\Symp(M\#n\overline{\mathbb{CP}^2},ω)$ are infinitely generated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Family Seiberg-Witten equation on Kahler surface and $π_i(\Symp)$ on multiple-point blow ups of Calabi-Yau surfaces Du, Yi Geometric Topology Symplectic Geometry Let $ω$ be a Kahler form on $M$, which is a torus $T^4$, a $K3$ surface or an Enriques surface, let $M\#n\overline{\mathbb{CP}^2}$ be $n-$point Kahler blowup of $M$. Suppose that $κ=[ω]$ satisfies certain irrationality condition. Applying techniques related to deformation of complex objects, we extend the guage-theoretic invariant on closed Kahler suraces developed by Kronheimer\cite{Kronheimer1998} and Smirnov\cite{Smirnov2022}\cite{Smirnov2023}. As a result, we show that even dimensional higher homotopy groups of $\Symp(M\#n\overline{\mathbb{CP}^2},ω)$ are infinitely generated. |
| title | Family Seiberg-Witten equation on Kahler surface and $π_i(\Symp)$ on multiple-point blow ups of Calabi-Yau surfaces |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2412.19375 |