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Abstract
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Let
be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric
satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian
is
essentially self-adjoint. We establish the asymptotic expansion for the resolvent trace
of
.
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
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Mathematical Subject Classification 2010
Primary: 35J75, 58J35
Secondary: 58J37
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Milestones
Received: 3 June 2019
Revised: 29 July 2020
Accepted: 29 November 2020
Published: 28 May 2021
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