Torsion-free

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