Ray-Singer type theorem for the refined analytic torsion

Braverman, M; Kappeler, T (2007). Ray-Singer type theorem for the refined analytic torsion. Journal of Functional Analysis, 243(1):232-256.

Abstract

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.

Abstract

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.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Physical Sciences > Analysis English 2007 09 Apr 2009 20:10 23 Jan 2022 13:58 Elsevier 0022-1236 Hybrid https://doi.org/10.1016/j.jfa.2006.10.008 http://arxiv.org/abs/math/0603638

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