Functoriality for higher rho invariants of elliptic operators
Functoriality for higher rho invariants of elliptic operators
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DOI：
10.1016/j.jfa.2021.108966
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发表时间：
2020-05
影响因子：
1.7
通讯作者：
Haoyang Guo;Zhizhang Xie;Guoliang Yu
中科院分区：
文献类型：
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作者：
Haoyang Guo;Zhizhang Xie;Guoliang Yu
设N是具有正标量曲率的闭自旋流形，DN是N上的狄拉克算子.设M1和M2是N的两个伽罗华复盖，使得M2是M1的商，则从M1到M2的商映射自然地诱导出与这两个流形相关的几何C⁎-代数之间的映射.我们用有限传播的方法证明了DN到M1和M2的升力的最大高阶Rho不变量关于上述商映射表现为泛函.这可用于高阶Rho不变量的计算，以及其他相关不变量的计算。
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 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.