On the index formula for singular surfaces
type: Item
instance of: scholarly article
title: On the index formula for singular surfaces
zbMATH Open document ID: 1032.58011
author: B.-W. Schulze
author: Boris V. Fedosov
author: N. N. Tarkhanov
published in: Pacific Journal of Mathematics
publication date: 2000-06-22T00:00:00Z
review text: The authors obtained the index formula for elliptic pseudodifferential operators on a 2-dimensional manifold with conical points which contains the Atiyah-Singer integral, the eta invariant and the other term expressed by the conormal principal and subprincipal symbols of the operator at the conical points. In this paper, they induce an explicit description of the contribution of a conical point for elliptic differential operators: By changing the origin in the complex plane they make the third term to vanish reducing the whole contribution of the conical point to the shifted eta invariant. They describe the eta invariant in terms of the monodromy index for an ordinary differential equation defined by the conormal symbol.
reviewed by: Yong Seung Cho
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58J28
zbMATH DE Number: 1463727
zbMATH Keywords: Index formula
zbMATH Keywords: singular surfaces
zbMATH Keywords: monodromy matrix
zbMATH Keywords: asymptotic solution
zbMATH Keywords: conical point for elliptic differential operators
zbMATH Keywords: eta invariant
MaRDI profile type: Publication
full work available at URL: pjm.1999.191.25
OpenAlex ID: W2002637364
DOI: 10.2140/PJM.1999.191.25
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description: scientific article; zbMATH DE number 1463727