nLab Reidemeister torsion




In perturbative Chern-Simons theory

appears in perturbative quantization of 3d Chern-Simons theory


An introduction and survey is in

  • L. Nicolaescu, Notes on Reidemeister torsion (pdf)

The notion of Reidemeister torsion originates in

  • Kurt Reidemeister, Automorphismen von Homotopiekettenringen, Math. Ann. 112 (1936), 586–593.

and was then extended in

  • W. Franz, Über die Torsion einer Überdeckung, J. Reine Angew. Math. 173 (1935), 245–254.

and in

  • Georges de Rham, Complexes á automorphismes et homéomorphie différentiable, Ann. Inst. Fourier (Grenoble) 2 (1950), 51–67.

Reidemeister torsion was identified with the Alexander polynomial in

  • John Milnor, A duality theorem for the Reidemeister torsion, Ann. of Math. 76 (1962),



  • Jeff Cheeger, Analytic torsion and the heat equation, Ann. of Math. 109 (1979), 259–322.


  • W. Müller, Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math. 28 (1978), 233–305.

proved that on compact Riemannian manifolds it coincides with analytic torsion.

Relation to the volume is discussed in

  • Pere Menal-Ferrer, Joan Porti, Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds (arXiv:1110.3718)

Relation to 3d-3d correspondence:

Last revised on December 28, 2019 at 18:12:18. See the history of this page for a list of all contributions to it.