Removing Metric Anomalies from Ray Singer Torsion

1998/07/02 by Dan Burghelea, Burghelea, Dan
Mathematics · #57Q10 #58G26 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:57Q10 #msc:58G26

paper · pdf · doi:10.48550/arxiv.math/9807007

10 pages, AMSTEX,typos corrected, thanks added

arxiv created 1998/07/29 · arxiv updated 2009/11/30

Abstract

Ray Singer torsion is a numerical invariant associated with a compact Riemannian manifold equipped with a flat bundle and a Hermitian structure on this bundle. In this note we show how one can remove the dependence on the Riemannian metric and on the Hermitian structure with the help of a base point and of an Euler structure, in order to obtain a topological invariant. A numerical invariant for an Euler structure and additional data is also constructed.

Related

• The Ray-Singer torsion
• A Refinement of the Ray-Singer Torsion
• Combinatorial invariants computing the Ray-Singer analytic torsion
• Refined Analytic Torsion
• Ray Singer Analytic Torsion of Calabi Yau manifolds I