Vol. 3, No. 1, 2021

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Resolvent trace asymptotics on stratified spaces

Luiz Hartmann, Matthias Lesch and Boris Vertman

Vol. 3 (2021), No. 1, 75–108
Abstract

Let (M,g) be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian Δ is essentially self-adjoint. We establish the asymptotic expansion for the resolvent trace of Δ. Our method proceeds by induction on the depth and applies in principle to a larger class of second-order differential operators of regular-singular type, e.g., Dirac Laplacians. Our arguments are functional analytic, do not rely on microlocal techniques and are very explicit. The results of this paper provide a basis for studying index theory and spectral invariants in the setting of smoothly stratified spaces and in particular allow for the definition of zeta-determinants and analytic torsion in this general setup.

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Keywords
resolvent trace asymptotics, stratified spaces, cone-edge metrics
Mathematical Subject Classification 2010
Primary: 35J75, 58J35
Secondary: 58J37
Milestones
Received: 3 June 2019
Revised: 29 July 2020
Accepted: 29 November 2020
Published: 28 May 2021
Authors
Luiz Hartmann
Universidade Federal de São Carlos
São Carlos
Brazil
Matthias Lesch
Universität Bonn
Bonn
Germany
Boris Vertman
Universität Oldenburg
Oldenburg
Germany