Abstract
We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold with coefficients in a flat complex vector bundle . We compute the Ray–Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on , we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual.
Citation
Maxim Braverman. Thomas Kappeler. "Refined analytic torsion as an element of the determinant line." Geom. Topol. 11 (1) 139 - 213, 2007. https://doi.org/10.2140/gt.2007.11.139
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