有边流形的L2-index定理
L2-index theorem for manifolds with boundary
摘要：
设M是一个带边界带边流形.设N是M的正规覆盖。设（A，T）是M上的椭圆型微分边值问题，其提升（\tilde A，\tilde T）到N.然后定义了该提升的核和上核的vonNeumann维数。本文的主要结果是：这些数是有限的，它们的差，根据定义冯诺依曼指数，等于（A，T）的指数。这样，我们将经典的Atiyah的L^2-指标定理推广到了有边流形。
英文摘要：
Suppose M is a compact manifold with boundary. Let N be a normal covering of M. Suppose (A,T) is an elliptic differential boundary value problem on M with lift (\tilde A,\tilde T) to N. Then the von Neumann dimension of kernel and cokernel of this lift are defined. The main result of this paper is: these numbers are finite, and their difference, by definition the von Neumann index, equals the index of (A,T). In this way, we extend the classical L^2-index theorem of Atiyah to manifolds with boundary.
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。
