Analytic Torsion and R-Torsion for Manifolds with Boundary

Details Analytic Torsion and R-Torsion for Manifolds with Boundary Analytic Torsion and R-Torsion for Manifolds with Boundary

1999-01-12

arxiv.org/abs/math/9901052v3

Mathematics

Differential Geometry

24 pages. to appear in Asian J. Math

Scientific paper

We prove a formula relating the analytic torsion and Reidemeister torsion on manifolds with boundary in the general case when the metric is not necessarily a product near the boundary. The product case has been established by W. Lu\"ck and S. M. Vishik. We find that the extra term that comes in here in the nonproduct case is the transgression of the Euler class in the even dimensional case and a slightly more mysterious term involving the second fundamental form of the boundary and the curvature tensor of the manifold in the odd dimensional case.

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