Analytic torsion

Summary

Analytic torsion, or Ray–Singer torsion, is a spectral invariant of a closed Riemannian manifold with an orthogonal or unitary representation of its fundamental group. It is an alternating product of zeta-regularized determinants of the Laplacians on forms with values in the associated flat bundle. Ray and Singer introduced it as an analytic counterpart of Reidemeister torsion, a combinatorial invariant that can distinguish homotopy equivalent lens spaces. The Cheeger–Müller theorem says that the two torsions agree.