nLab Reidemeister torsion

Idea

(…)

Properties

In perturbative Chern-Simons theory

appears in perturbative quantization of 3d Chern-Simons theory

Related concepts

• analytic torsion

References

Introduction and survey:

• 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),

  137–147.

Proof that, on compact Riemannian manifolds, Reidemeister torsion coincides with analytic torsion:

• Jeff Cheeger: Analytic torsion and Reidemeister torsion, Proc. Natl. Acad. Sci. USA 74 7 (1977) 2651-2654 [doi:10.1073/pnas.74.7.2651, pdf]

• Werner Müller: Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math. 28 3 (1978) 233-305 [doi;10.1016/0001-8708(78)90116-0]

Relation to the volume of hyperbolic 3-manifold:

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

Relation to 3d-3d correspondence:

• Dongmin Gang, Seonhwa Kim, Seokbeom Yoon, Adjoint Reidemeister torsions from wrapped M5-branes (arXiv:1911.10718)