Refined analytic torsion: comparison theorems and examples
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Bibliographic record
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 [BK1, Remark 14.9].
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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