Vol. 15, No. 3, 2022

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A Cheeger–Müller theorem for manifolds with wedge singularities

Pierre Albin, Frédéric Rochon and David Sher

Vol. 15 (2022), No. 3, 567–642
Abstract

We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided the Hodge Laplacians in the fibers of the wedge have an appropriate spectral gap, we give uniform constructions of the resolvent and heat kernel on suitable manifolds with corners. When the wedge manifold and the base of the wedge are odd-dimensional, this is used to obtain a Cheeger–Müeller theorem relating analytic torsion with the Reidemeister torsion of the natural compactification by a manifold with boundary.

Keywords
analytic torsion, wedge metrics, resolvent, heat kernel
Mathematical Subject Classification 2010
Primary: 58J05, 58J35, 58J52
Secondary: 55N25
Milestones
Received: 15 August 2018
Revised: 19 August 2020
Accepted: 28 October 2020
Published: 10 June 2022
Authors
Pierre Albin
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Frédéric Rochon
Département de Mathématiques
UQÀM
Montreal, QC
Canada
David Sher
Department of Mathematical Sciences
DePaul University
Chicago, IL
United States