# nLab torsion

The term torsion can denote very different concepts:

Usually there is no risk of confusion, since these terms are used in very different areas of mathematics. Except maybe for the following situation:

• when a $U(1)$-gerbe on a manifold $X$ is used as the background field of a sigma-model for conformal field theory, its curvature 3-form characterizes the torsion – in the differential geometric sense – of a connection induced on the tangent space of $X$ from the coresponding 2-spectral triple. At the same time, it is of interest whether the characteristic class of the gerbe, which is an element in $H^3(X, \mathbb{Z})$ is a torsion element in the sense of group theory. Authors in this area will often say sentences like “The gerbe is torsion.” which may sound ambiguous for this reason. But if the author knows what a gerbe is, he or she almost surely means the group-theoretic sense.

category: disambiguation

Revised on December 18, 2014 14:54:02 by Urs Schreiber (127.0.0.1)