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arXiv · 1810.04204

Resolvent Trace Asymptotics on Stratified Spaces

Luiz Hartmann·Matthias Lesch·Boris Vertman
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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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Luiz Hartmann, Matthias Lesch, Boris Vertman. 2018-10-09. Resolvent Trace Asymptotics on Stratified Spaces. https://doi.org/10.2140/paa.2021.3.75

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