Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps

作者：Pfaff Jonathan^*

来源：Mathematische Zeitschrift, 2014, 277(3-4): 953-974.

DOI：10.1007/s00209-014-1287-5

• Analytic torsion
• Selberg and Ruelle zeta functions
• Reidemeister torsion
• Cheeger-Muller theorem

For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of to the corresponding Reidemeister torsion. While the analytic torsion is a spectral invariant of the manifold, the Reidemeister torsion is of combinatorial nature. Our proof rests on an expression of the analytic torsion in terms of special values of Ruelle zeta functions as well as on recent work of Pere Menal-Ferrer and Joan Porti.

• 出版日期2014-8