Refined analytic torsion: comparison theorems and examples

Details Refined analytic torsion: comparison theorems and examples Refined analytic torsion: comparison theorems and examples

2006-02-10

arxiv.org/abs/math/0602231v2

Mathematics

Differential Geometry

15 pages. To appear in Illinois Journal of Mathematics

Scientific paper

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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