Analytic torsion and Reidemeister torsion.
We announce a proof of the conjecture of Ray and Singer that for a compact Riemannian manifold the analytic torsion and Reidemeister torsion are equal. The proof involves studying the heat equation for certain manifolds M, equipped with metrics g(u), 0 < u < 1 which degenerate in a prescribed way at the boundary deltaM, as u --> 0,1.
Cheeger
J
J
Department of Mathematics, State University of New York, Stony Brook, New York 11794.