论文标题
4个manifolds中嵌入式表面的同位素的邻接不平等阻塞
An adjunction inequality obstruction to isotopy of embedded surfaces in 4-manifolds
论文作者
论文摘要
考虑一个光滑的$ 4 $ - manifold $ x $和一个差异$ f：x \ to x $。我们以$ x $的嵌入式表面的相邻不平等的形式给出了障碍物，以在$ f $下的图像同位素。因此，代表给定同源性类别的表面的最小属，其在$ f $下的图像同位素通常大于没有同位素条件的最小属。我们举例说明不平等严格。我们使用障碍物来构建无限多个嵌入式表面的实例，这些表面都是连续的同位素，但平稳地相互异位。
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.
