The analytic torsion of a cone over an odd dimensional manifold

Author(s)

Hartmann, L. ^[1] ; Spreafico, M. ^[2]

Affiliation

^[1] Univ Fed Sao Carlos, UFSCar, BR-13560 Sao Carlos, SP - Brazil

^[2] Univ Sao Paulo, ICMC, BR-05508 Sao Paulo - Brazil

• Document type: Journal article
• Source: JOURNAL OF GEOMETRY AND PHYSICS; v. 61, n. 3, p. 624-657, MAR 2011.
• Web of Science Citations: 9

Abstract

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem {[}3, 2] for a manifold with boundary, according to Bruning and Ma (2006) {[}5]. We also prove Poincare duality for the analytic torsion of a cone. (C) 2010 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 09/15145-9 - Reidemeister torsion and analytic torsion of spaces with conical singularities
• Grantee: Luiz Roberto Hartmann Junior
• Support Opportunities: Scholarships in Brazil - Post-Doctoral