论文标题
kervaire的Sphere-link在同型4-Sphere中的缎带及其对2个复合物的后果
Ribbonness of Kervaire's sphere-link in homotopy 4-sphere and its consequences to 2-complexes
论文作者
论文摘要
M. A. Kervaire表明，每组不足$ D $和重量$ d $都是平滑的$ D $组件的基本组，在平滑的同型4-Sphere中。在使用光滑的解开猜想和光滑的4D Poincar {é}猜想时，任何此类球形链接都显示为4-Sphere中自由色带球形链接的螺旋链接。由于4个球体中的每个色带球链接也被证明是4个球体中的自由色带球链接的斜向键，因此Kervaire的球体链接和色带球链接是等效的概念。通过将此结果应用于4盘中的色带磁盘链接，可以表明4盘中每个带状磁盘 - 连接的紧凑型补体都是非球体的。通过此属性，引入了每个可违约有限的2复合物的带磁链接呈现。通过使用此演示文稿，可以证明每个连接的有限2-复合物的连接子复杂性都是非球面的（对于白人非球形猜想而言，部分意思是是的）。
M. A. Kervaire showed that every group of deficiency $d$ and weight $d$ is the fundamental group of a smooth sphere-link of $d$ components in a smooth homotopy 4-sphere. In the use of the smooth unknotting conjecture and the smooth 4D Poincar{é} conjecture, any such sphere-link is shown to be a sublink of a free ribbon sphere-link in the 4-sphere. Since every ribbon sphere-link in the 4-sphere is also shown to be a sublink of a free ribbon sphere-link in the 4-sphere, Kervaire's sphere-link and the ribbon sphere-link are equivalent concepts. By applying this result to a ribbon disk-link in the 4-disk, it is shown that the compact complement of every ribbon disk-link in the 4-disk is aspherical. By this property, a ribbon disk-link presentation for every contractible finite 2-complex is introduced. By using this presentation, it is shown that every connected subcomplex of a contractible finite 2-complex is aspherical (meaning partially yes for Whitehead aspherical conjecture).
