Analytic surgery and the accumulation of eigenvalues
type: Item
instance of: scholarly article
title: Analytic surgery and the accumulation of eigenvalues
zbMATH Open document ID: 0854.58039
author: Andrew Hassell
author: Rafe Mazzeo
author: Richard Melrose
published in: Communications in Analysis and Geometry
publication date: 1996-03-17T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 856914
zbMATH Keywords: manifolds with corners
zbMATH Keywords: \(b\)-fibrations
zbMATH Keywords: eta invariant
zbMATH Keywords: eigenvalues
reviewed by: Mircea Puta
MaRDI profile type: Publication
DOI: 10.4310/CAG.1995.V3.N1.A4
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description: scientific article; zbMATH DE number 856914