A Refinement of the Ray-Singer Torsion
Abstract
This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. The refined analytic torsion is a holomorphic function of the representation of the fundamental group. When the representation is unitary, the absolute value of the refined analytic torsion is equal to the Ray-Singer torsion, while its phase is determined by the eta-invariant. The fact that the Ray-Singer torsion and the eta-invariant can be combined into one holomorphic function allows to use methods of complex analysis to study both invariants.
Cite
@article{arxiv.math/0509578,
title = {A Refinement of the Ray-Singer Torsion},
author = {Maxim Braverman and Thomas Kappeler},
journal= {arXiv preprint arXiv:math/0509578},
year = {2007}
}
Comments
6 pages, to apper in Comptes rendus Acad. Sci. Paris