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Refined analytic torsion: comparison theorems and examples

Rung-Tzung Huang
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Abstract

Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. Using this result we establish, modulo sign, the Burghelea-Haller conjecture, comparing their complex analytic torsion with Farber-Turaev torsion in the case, when the flat connection can be deformed in the space of flat connections to a Hermitian connection. We also compute the refined analytic torsion of lens spaces.

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Rung-Tzung Huang. 2006-10-20. Refined analytic torsion: comparison theorems and examples. https://arxiv.org/abs/math/0602231

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