The metric anomaly of analytic torsion at the boundary of an even dimensional cone
type: Item
instance of: scholarly article
title: The metric anomaly of analytic torsion at the boundary of an even dimensional cone
zbMATH Open document ID: 1235.58026
author: Boris Vertman
published in: Annals of Global Analysis and Geometry
publication date: 2012-01-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1004.2069
review text: The formula for analytic torsion of a cone in even dimensions involves three terms. The first two terms are well understood and are given by an algebraic combination of the Betti numbers and the analytic torsion of the base of the cone. The third ``singular'' contribution is an intricate spectral invariant of the cone base. The author identifies the third term as the metric anomaly of the analytic torsion coming from the non-product structure of the cone at its regular boundary. The author filters out the contribution of the conical singularity and identifies the analytic torsion of an even-dimensional cone purely in terms of the Betti numbers and the analytic torsion of the cone base.
Mathematics Subject Classification ID: 58J52
zbMATH DE Number: 5996717
zbMATH Keywords: analytic torsion
zbMATH Keywords: conical singularities
zbMATH Keywords: bounded generalized cone
zbMATH Keywords: metric anomaly
zbMATH Keywords: Cheeger-Müller theorem
reviewed by: Michael Farber
MaRDI profile type: Publication
OpenAlex ID: W2083935886
arXiv ID: 1004.2069
cites work: Q3785142
cites work: Zeta function determinant of the Laplace operator on the \(D\)-dimensional ball
cites work: Heat-kernels and functional determinants on the generalized cone
cites work: An anomaly formula for Ray-Singer metrics on manifolds with boundary
cites work: An Index Theorem for First Order Regular Singular Operators
cites work: On the Determinant of Elliptic Boundary Value Problems on a Line Segment
cites work: Analytic torsion and Reidemeister torsion
cites work: Spectral geometry of singular Riemannian spaces
cites work: Intersection R-torsion and analytic torsion for pseudomanifolds
cites work: Reidemeister torsion and analytic torsion of spheres
cites work: Complexes à automorphismes et homéomorphic différentiable
cites work: Spinors and forms on the ball and the generalized cone
cites work: Über die Torsion einer Überdeckung.
cites work: The analytic torsion of a cone over a sphere
cites work: The analytic torsion of a cone over an odd dimensional manifold
cites work: Determinants of Regular Singular Sturm - Liouville Operators
cites work: Analytic and topological torsion for manifolds with boundary and symmetry
cites work: Analytic torsion and R-torsion of Riemannian manifolds
cites work: The Metric Anomaly of Analytic Torsion on Manifolds with Conical Singularities
cites work: Problèmes mixtes pour le système de Maxwell
cites work: R-torsion and the Laplacian on Riemannian manifolds
cites work: Homotopieringe und Linsenräume
cites work: Zeta function and regularized determinant on a disc and on a cone
cites work: Zeta invariants for Dirichlet series
cites work: Analytic torsion of a bounded generalized cone
cites work: Zeta determinants for regular-singular Laplace-type operators
cites work: Generalized Ray-Singer conjecture. I: A manifold with a smooth boundary
cites work: Q3873024
DOI: 10.1007/S10455-011-9271-3
description: scientific article