Mathematics – Dynamical Systems
Scientific paper
2005-09-24
Mathematics
Dynamical Systems
6 pages, to apper in Comptes rendus Acad. Sci. Paris
Scientific paper
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.
Braverman Maxim
Kappeler Thomas
No associations
LandOfFree
A Refinement of the Ray-Singer Torsion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Refinement of the Ray-Singer Torsion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Refinement of the Ray-Singer Torsion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-552951