论文标题
椭圆运算符的较高Rho不变性的功能
Functoriality for higher rho invariants of elliptic operators
论文作者
论文摘要
让$ n $是带有正标曲率的封闭旋转歧管，$ n $ d_n $ the $ n $。令$ m_1 $和$ m_2 $为$ n $的两个galois封面，这样$ m_2 $是$ m_1 $的商。然后，商图从$ m_1 $到$ m_2 $自然诱导了与两个歧管相关的几何$ c^*$ - 代数之间的地图。我们通过有限的宣传参数证明了\ emph {maximal} $ d_n $的升降机的较高rho不变式，至$ m_1 $，而$ m_2 $相对于上述商映射，其功能性。这可以应用于较高Rho不变性的计算以及其他相关的不变式。
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.
