4-流形中嵌入曲面同痕的一个伴随不等式障碍
An adjunction inequality obstruction to isotopy of embedded surfaces in 4-manifolds
AI总结：
本文提出一个伴随不等式障碍，用于判断4-流形中嵌入曲面在微分同胚下是否同痕，并据此构造了无限多个连续同痕但彼此不光顺同痕的嵌入曲面例子。
摘要：
考虑一个光滑 $4$-流形 $X$ 和一个微分同胚 $f : X \ o X$。我们给出了一个以伴随不等式为形式的障碍，用于判断 $X$ 中的嵌入曲面是否同痕于其在 $f$ 下的像。由此可得，表示给定同调类且同痕于其在 $f$ 下像的曲面的最小亏格，通常大于无同痕条件下的最小亏格。我们给出了不等式严格成立的例子。我们利用该障碍构造了无限多个嵌入曲面的例子，它们均连续同痕但彼此不光顺同痕。
英文摘要：
Consider a smooth $4$-manifold $X$ and a diffeomorphism $f : X \to X$. We give an obstruction in the form of an adjunction inequality for an embedded surface in $X$ to be isotopic to its image under $f$. It follows that the minimal genus of a surface representing a given homology class and which is isotopic to its image under $f$ is generally larger than the minimal genus without the isotopy condition. We give examples where the inequality is strict. We use our obstruction to construct examples of infinitely many embedded surfaces which are all continuously isotopic but mutually non-isotopic smoothly.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
