论文标题
自指的椎间盘和灯泡引理
Self-Referential Discs and the Light Bulb Lemma
论文作者
论文摘要
我们展示了4个manifolds中的自指盘是如何导致与圆盘的构造，该碟片具有共同的几何双球体，这些圆盘是同型$ \ partial $，一致且重合其边界附近，但没有适当的同位素。这发生在其基本群体中没有2个扭转的流形中，例如$ s^2 \ times d^2 $和$ s^1 \ times b^3 $的边界连接总和，从而表现出没有球形的现象。另一方面，我们表明，如果流形仅连接，则两个这样的光盘是同位素re $ \ partial $。我们以$ s^2 \ times d^2 \自然s^1 \ times b^3 $ a构建，适当地嵌入3孔的3球与$ z_0 \ times b^3 $适当地均匀，但不能适当地同位素到$ z_0 \ z_0 \ times b^3 $。
We show how self-referential discs in 4-manifolds lead to the construction of pairs of discs with a common geometrically dual sphere which are homotopic rel $\partial$, concordant and coincide near their boundaries, yet are not properly isotopic. This occurs in manifolds without 2-torsion in their fundamental group, e.g. the boundary connect sum of $S^2\times D^2$ and $S^1\times B^3$, thereby exhibiting phenomena not seen with spheres. On the other hand we show that two such discs are isotopic rel $\partial$ if the manifold is simply connected. We construct in $S^2\times D^2\natural S^1\times B^3$ a properly embedded 3-ball properly homotopic to a $z_0\times B^3$ but not properly isotopic to $z_0\times B^3$.
