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| Real analytic torsion is a spectral invariant of a compact Riemannian manifold
equipped with a flat Hermitian vector bundle, that was introduced by Ray-Singer in 1971.
Ray and Singer conjectured that for unitarily flat vector bundles,
this invariant coincides with the Reidemeister torsion, a topological invariant.
This conjecture was established by Cheeger and Mueller, and extended by Bismut-Zhang to
arbitrary flat vector bundles. We derive the Bismut-Zhang theorem
for manifolds with boundary and the gluing
formula for the analytic torsion of flat vector bundles in full
generality, i.e., we do not assume that the Hermitian metric on the flat vector bundle
is flat nor that the Riemannian metric has product structure
near the boundary. |
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