Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Reidemeister torsion (or R-torsion, or Reidemeister-Franz torsion) is a topological invariant of manifolds introduced by Reidemeister (1935) for 3- manifolds and generalized to higher dimensions by Franz (1935) and de Rham (1936). Analytic torsion (or Ray-Singer torsion) is an invariant of Riemannian manifolds defined by Ray and Singer (1971, 1973a, 1973b) as an analytic analogue of Reidemeister torsion. Cheeger (1977, 1979) and Muller (1978) proved Ray and Singer's conjecture that Reidemeister torsion and analytic torsion are the same for compact Riemannian manifolds.

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