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Refined analytic torsion

2008
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Journal of differential geometry
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Given an acyclic representation α of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to an acyclic unitary representation, we define a refinement Tα of the Ray-Singer torsion associated to α, which can be viewed as the analytic counterpart of the refined combinatorial torsion introduced by Turaev. Tα is equal to the graded determinant of the odd signature operator up to a correction term, the metric anomaly, needed to make it independent of the choice

doi:10.4310/jdg/1203000267
fatcat:qeaqn6mxmjdktbzzbr75jbvwhu