nLab
Reidemeister torsion
Idea
(…)
Properties
In perturbative Chern-Simons theory
appears in perturbative quantization of 3d Chern-Simons theory
References
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),
137–147.
Then
- Jeff Cheeger, Analytic torsion and the heat equation, Ann. of Math. 109 (1979), 259–322.
and
- 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.
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