Refined analytic torsion: Comparison theorems and examples

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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 the Farber-Turaev refinement of the combinatorial torsion. Using this result we establish, modulo sign, the Burghelea-Haller conjecture, comparing their complex analytic torsion with the Farber-Turaev torsion in the case when the flat connection can be deformed in the space of flat connections to a Hermitian connection. We then compute the refined analytic torsion of lens spaces and answer some of the questions posed in [5, Remark 14.9].

Original languageEnglish
Pages (from-to)1309-1327
Number of pages19
JournalIllinois Journal of Mathematics
Volume51
Issue number4
DOIs
StatePublished - 2008

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