规范群的$A_\infty$ -型的无限性
Infiniteness of $A_\infty$-types of gauge groups
摘要：
设$G$是紧连通李群，$P$是$K$上的主$G$ -丛. $P$的规范群是$P$的自同构的拓扑群。对于固定的$G$和$K$，考虑$K$上的所有主$G$ -束$P$。Crabb-Sutherland和第二作者证明了：如果$n<\infty$和$K$是有限复形，则$P$的规范群的$A_n$型的个数是有限的.证明了当$K$是球面且有无穷多个$P$时，$P$的规范群的$A_\infty$型数是无穷的.
英文摘要：
Let $G$ be a compact connected Lie group and let $P$ be a principal $G$-bundle over $K$. The gauge group of $P$ is the topological group of automorphisms of $P$. For fixed $G$ and $K$, consider all principal $G$-bundles $P$ over $K$. It is proved by Crabb--Sutherland and the second author that the number of $A_n$-types of the gauge groups of $P$ is finite if $n<\infty$ and $K$ is a finite complex. We show that the number of $A_\infty$-types of the gauge groups of $P$ is infinite if $K$ is a sphere and there are infinitely many $P$.
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。
