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<p>Given a compact, oriented, connected surface <i>F</i>, we show that the set of connected sutured manifolds (<i>M</i>, <i>γ</i>) with <i>R</i><sub>±</sub>(<i>γ</i>) ≌ <i>F</i> is generated by the product sutured manifold (<i>F</i>, <i>∂F</i>) × [0, 1] through surgery triads. This result has applications in Floer theories of 3-manifolds. The special case where <i>F</i> = <i>D</i><sup>2</sup> or <i>F</i> = <i>S</i><sup>2</sup> has been a folklore theorem, which has already been used by experts before.</p>

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Generation of sutured manifolds

  • 期刊论文

  • 发表日期：

    2025年8月27日

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  • Yi Ni

摘要

Given a compact, oriented, connected surface F, we show that the set of connected sutured manifolds (M, γ) with R±(γ) ≌ F is generated by the product sutured manifold (F, ∂F) × [0, 1] through surgery triads. This result has applications in Floer theories of 3-manifolds. The special case where F = D2 or F = S2 has been a folklore theorem, which has already been used by experts before.