Refined analytic torsion on manifolds with boundary

Vertman, Boris¹

¹ Department of Mathematics, University of Bonn, Beringstr. 6, 53115 Bonn, Germany

Geometry & topology, Tome 13 (2009) no. 4, pp. 1989-2027.

Résumé

We discuss the refined analytic torsion, introduced by M Braverman and T Kappeler as a canonical refinement of analytic torsion on closed manifolds. Unfortunately there seems to be no canonical way to extend their construction to compact manifolds with boundary. We propose a different refinement of analytic torsion, similar to Braverman and Kappeler, which does apply to compact manifolds with and without boundary. In a subsequent publication we prove a surgery formula for our construction.

Détail

DOI : 10.2140/gt.2009.13.1989

Keywords: refined analytic torsion, ideal boundary condition, non-self-adjoint operator

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