In mathematics, torsion-free may refer to:
Abstract algebra
Torsion-free group, a group whose only element of finite order is the identity Torsion-free module, module over an integral domain where zero is the only torsion element Torsion-free abelian group, an abelian group which is a torsion-free group Torsion-free rank, the cardinality of a maximal linearly independent subset of an abelian group or of a module over an integral domain
Differential geometry Torsion-free affine connection, an affine connection whose torsion tensor vanishes Torsion-free metric connection or Levi-Civita connection, a unique symmetric connection on the tangent bundle of a manifold compatible with the metric
See also Torsion (disambiguation)