Betti numbers are used in algebraic topology to count the number of independent cycles of different dimensions in a space. They are named after the Italian mathematician Enrico Betti.

Given a topological space, its homology groups can contain elements of infinite order (free part) and elements of finite order (torsion part). The presence of torsion elements indicates certain structural or topological properties of the space.

In differential geometry, torsion is associated with the twisting of a space curve. Specifically, it measures how a curve deviates from being planar.