椭圆算子高阶rho不变量的函子性
Functoriality for higher rho invariants of elliptic operators
AI总结：
本文通过有限传播论证证明了具有正数量曲率的闭spin流形上Dirac算子的高阶rho不变量在Galois覆盖商映射下具有函子性，并应用于相关不变量的计算。
摘要：
设$N$为具有正数量曲率的闭spin流形，$D_N$为$N$上的Dirac算子。设$M_1$和$M_2$是$N$的两个Galois覆盖，且$M_2$是$M_1$的商。则从$M_1$到$M_2$的商映射自然地诱导出与这两个流形相关联的几何$C^*$-代数之间的映射。我们通过有限传播论证证明，$D_N$提升到$M_1$和$M_2$上的\emph{极大}高阶rho不变量关于上述商映射具有函子性。这可应用于高阶rho不变量及其他相关不变量的计算。
英文摘要：
Let $N$ be a closed spin manifold with positive scalar curvature and $D_N$ the Dirac operator on $N$. Let $M_1$ and $M_2$ be two Galois covers of $N$ such that $M_2$ is a quotient of $M_1$. Then the quotient map from $M_1$ to $M_2$ naturally induces maps between the geometric $C^*$-algebras associated to the two manifolds. We prove, by a finite-propagation argument, that the \emph{maximal} higher rho invariants of the lifts of $D_N$ to $M_1$ and $M_2$ behave functorially with respect to the above quotient map. This can be applied to the computation of higher rho invariants, along with other related invariants.
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。
