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Comparison of the refined analytic and the Burghelea-Haller torsions

Maxim Braverman[1]; Thomas Kappeler[2]

  • [1] Northeastern University Department of Mathematics Northeastern University Boston, MA 02115 (USA)
  • [2] Universität Zürich Institut für Mathematik Winterthurerstrasse 190 8057 Zürich (Switzerland)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 7, page 2361-2387
  • ISSN: 0373-0956

Abstract

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The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form τ on the determinant line of the cohomology. Both τ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to ± τ . As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating their torsion with the square of the Farber-Turaev combinatorial torsion.

How to cite

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Braverman, Maxim, and Kappeler, Thomas. "Comparison of the refined analytic and the Burghelea-Haller torsions." Annales de l’institut Fourier 57.7 (2007): 2361-2387. <http://eudml.org/doc/10300>.

@article{Braverman2007,
abstract = {The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $\tau $ on the determinant line of the cohomology. Both $\tau $ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to $\pm \tau $. As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating their torsion with the square of the Farber-Turaev combinatorial torsion.},
affiliation = {Northeastern University Department of Mathematics Northeastern University Boston, MA 02115 (USA); Universität Zürich Institut für Mathematik Winterthurerstrasse 190 8057 Zürich (Switzerland)},
author = {Braverman, Maxim, Kappeler, Thomas},
journal = {Annales de l’institut Fourier},
keywords = {Determinant line; analytic torsion; Ray-Singer torsion; eta-invariant; Turaev torsion and Farber-Turaev torsion; determinant line; Turaev torsion; Farber-Turaev torsion},
language = {eng},
number = {7},
pages = {2361-2387},
publisher = {Association des Annales de l’institut Fourier},
title = {Comparison of the refined analytic and the Burghelea-Haller torsions},
url = {http://eudml.org/doc/10300},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Braverman, Maxim
AU - Kappeler, Thomas
TI - Comparison of the refined analytic and the Burghelea-Haller torsions
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 7
SP - 2361
EP - 2387
AB - The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $\tau $ on the determinant line of the cohomology. Both $\tau $ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to $\pm \tau $. As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating their torsion with the square of the Farber-Turaev combinatorial torsion.
LA - eng
KW - Determinant line; analytic torsion; Ray-Singer torsion; eta-invariant; Turaev torsion and Farber-Turaev torsion; determinant line; Turaev torsion; Farber-Turaev torsion
UR - http://eudml.org/doc/10300
ER -

References

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