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Description

The Cheeger-Muller theorem, first conjectured by Ray and Singer in 1973, gives equality between the analytic torsion and the Reidemeister torsion on a Riemannian manifold equipped with a flat Euclidean vector bundle. We prove a version of the Cheeger-Muller theorem on manifolds with cusp singularities. The proof uses geometric microlocal analysis techniques pioneered by Melrose, in particular the method of analytic surgery: we consider a family of smooth manifolds which degenerate to a manifold with cusps and study the behavior of the torsion under this degeneration. This is joint work with P. Albin (UIUC) and F. Rochon (UQAM).