Turaev torsion
= Turaev torsion
{c}
{wiki=Reidemeister_torsion}
Turaev torsion is a sign-refined form of Reidemeister torsion for manifolds and chain complexes. For a knot exterior with meridian $\mu$ and first Betti number one, its group-ring normalization satisfies
$$
\tau(X_K)\doteq\frac{\Delta_K}{1-[\mu]}.
$$