L2-index Theorem for Elliptic Differential Boundary Problems

نویسندگان

  • Thomas Schick
  • THOMAS SCHICK
چکیده

Suppose M is a compact manifold with boundary ∂M . Let M̃ be a normal covering of M . Suppose (A, T ) is an elliptic differential boundary value problem on M with lift (Ã, T̃ ) to M̃ . 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 of (Ã, T̃ ), equals the index of (A, T ). In this way, we extend the classical L-index theorem of Atiyah to elliptic differential boundary value problems.

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تاریخ انتشار 2001