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)

Topics referred to by the same term

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