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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Refined analytic torsion on manifolds with boundary

Boris Vertman

Geometry & Topology 13 (2009) 1989–2027
Abstract

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.

Keywords
refined analytic torsion, ideal boundary condition, non-self-adjoint operator
Mathematical Subject Classification 2000
Primary: 58J52
References
Publication
Received: 17 August 2008
Revised: 17 March 2009
Accepted: 13 February 2009
Published: 26 April 2009
Proposed: Tobias Colding
Seconded: David Gabai, Gang Tian
Authors
Boris Vertman
Department of Mathematics
University of Bonn
Beringstr. 6
53115 Bonn
Germany