华东师范大学几何研讨班

Abstract: In this talk, we introduce the Ray-Singer analytic torsion as the determinant of Laplace operators and the extended Cheeger-Mueller Theorem by Bismut-Zhang which gives the explicit relation between the Ray-Singer analytic torsion and the Reidemeister torsion. Note that the Reidemeister torsion is the first topological invariant in the history distinguishing the homotopy equivalent but not homeomorphic manifolds. At last, we explain the complex valued torsion, Burghelea-Haller torsion and Cappell-Miller torsion, and the resent results by Liu-Yu and Su-Zhang.