Analytic surgery and the accumulation of eigenvalues
In the paper under review a glueing formula for the eta invariant is presented. It is obtained by studying the full resolvent family of generalized Laplacians for metrics degenerating by surgery, and includes the analysis of accumulation of eigenvalues at the bottom of the continuous spectrum of \(\Delta_0\). From an analytic perspective the main result of this paper is the precise description of the form of the degeneracy of the resolvent family of the Laplacian (or Dirac operator) as the parameter \(\varepsilon \to 0\). This is encoded in the description of the resolvent as an element of an algebra of pseudodifferential operators with properties tailored to the geometry of the degeneration.
scientific article; zbMATH DE number 856914