论文标题
cobordism削减和粘贴组的K理论谱
A K-theory spectrum for cobordism cut and paste groups
论文作者
论文摘要
在不结合结合下，在多种歧管上施加了两种不同的关系，因此获得了歧管的群体和裁切的歧管群体。通过同时施加两种关系，定义了COBORDISM剪切和粘贴组$ \ overline {\ mathrm {sk}} _ n $。在本文中，我们将此定义扩展到歧管，并获得边界获得$ \ edline {\ mathrm {sk}}}^{\ partial} _n $，并研究了该组与适当定义的cobordism cobordism cobordism群的关系。主要结果是构建频谱的构造，该频谱在$π_0$上恢复了COBORDISM切割和粘贴带边界的歧管，$ \ overline {\ mathrm {sk}}^{\ partial} _n $，以及启动规范映射$ \ mathrm mathrm {skrm {sk}的光谱地图\ edline {\ mathrm {sk}}}^{\ partial} _n $。
Cobordism groups and cut-and-paste groups of manifolds arise from imposing two different relations on the monoid of manifolds under disjoint union. By imposing both relations simultaneously, a cobordism cut and paste group $\overline{\mathrm{SK}}_n$ is defined. In this paper, we extend this definition to manifolds with boundary obtaining $\overline{\mathrm{SK}}^{\partial}_n$ and study the relationship of this group to an appropriately defined cobordism group of manifolds with boundary. The main results are the construction of a spectrum that recovers on $π_0$ the cobordism cut and paste groups of manifolds with boundary, $\overline{\mathrm{SK}}^{\partial}_n$, and a map of spectra that lifts the canonical quotient map $\mathrm{SK}^{\partial}_n \rightarrow \overline{\mathrm{SK}}^{\partial}_n$.
