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<p>In the symplectic mapping class group of a 4-dimensional Weinstein domain, we give a relation between two products of (right-handed) Dehn twists via holomorphic curve techniques. A key ingredient of the construction is a solution to the symplectic isotopy problem on symplectic submanifolds in del Pezzo surfaces. In the appendix, we provide an alternative proof of a relation between a fibered Dehn twist and a product of Dehn twists.</p>

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A four-dimensional mapping class group relation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月17日

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  • Takahiro Oba

摘要

In the symplectic mapping class group of a 4-dimensional Weinstein domain, we give a relation between two products of (right-handed) Dehn twists via holomorphic curve techniques. A key ingredient of the construction is a solution to the symplectic isotopy problem on symplectic submanifolds in del Pezzo surfaces. In the appendix, we provide an alternative proof of a relation between a fibered Dehn twist and a product of Dehn twists.