Refined analytic torsion as an element of the determinant line

Braverman, M; Kappeler, T (2007). Refined analytic torsion as an element of the determinant line. Geometry & Topology, 11:139-213.

Abstract

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray–Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual.

Abstract

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray–Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual.

Statistics

Citations

Dimensions.ai Metrics
19 citations in Web of Science®
18 citations in Scopus®

Altmetrics

Detailed statistics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2007 07 Dec 2009 12:17 24 Sep 2019 16:15 Mathematical Sciences Publishers 1364-0380 Hybrid https://doi.org/10.2140/gt.2007.11.139 http://arxiv.org/abs/math/0510532

Preview
Filetype: PDF (Verlags-PDF)
Size: 1MB
View at publisher
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 4)
Size: 682kB
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 3)
Size: 660kB
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 2)
Size: 660kB
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 1)
Size: 650kB