Ray-Singer Type Theorem for the Refined Analytic Torsion
摘要
We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber-Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber-Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology.
引用
@article{arxiv.math/0603638,
title = {Ray-Singer Type Theorem for the Refined Analytic Torsion},
author = {Maxim Braverman and Thomas Kappeler},
journal= {arXiv preprint arXiv:math/0603638},
year = {2007}
}
备注
To appear in Journal of Functional Analysis The definition of the refined torsion was slightly changed, which made it more invariant, some references and remarks are added