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Complex valued Ray–Singer torsion II
Author(s) -
Burghelea Dan,
Haller Stefan
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910122
Subject(s) - mathematics , torsion (gastropod) , hermitian matrix , pure mathematics , degenerate energy levels , bilinear interpolation , mathematical analysis , algebra over a field , physics , quantum mechanics , medicine , statistics , surgery
In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian metrics to nonselfadjoint Laplacians based on fiber wise non‐degenerate symmetric bilinear forms. As an application we show that results about the asymptotics of the Ray–Singer torsion of self‐adjoint Witten deformation, as well as the strategy proposed by Burghelea–Friedlander–Kappeler to derive the comparison of Ray–Singer and Reidemeister torsion, can be extended to nonself‐adjoint Witten deformation. This is then used to conclude the equality of complex analytic and Milnor–Turaev torsion, at least for odd dimensional manifolds, up to sign (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)