Refined analytic torsion as an element of the determinant line

Braverman, Maxim¹ ; Kappeler, Thomas²

¹ Department of Mathematics, Northeastern University, Boston MA 02115, USA
² Institut fur Mathematik, Universitat Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

Geometry & topology, Tome 11 (2007) no. 1, pp. 139-213.

Résumé

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.

Détail

DOI : 10.2140/gt.2007.11.139

Keywords: determinant line, Ray–Singer, eta-invariant, analytic torsion

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