A T-fold is a space that locally looks like a Riemannian manifold equipped with a B-field, but is glued together from these not just by diffeomorphisms but also by T-duality transformations.

The idea is that a T-fold is a target space for a string sigma-model that is only locally a Riemannian manifold but globally a more general kind of geometry. In the literature sometimes the term non-geometric backgrounds is used for such “generalized geometric” backgrounds.


The idea was originally introduced in

Further developments are in

A precise global definition of T-folds as principal 2-bundles for the T-duality 2-group described in the nLab entry T-Duality and Differential K-Theory is given in

  • Thomas Nikolaus, T-Duality in K-theory and elliptic cohomology, talk at String Geometry Network Meeting, Feb 2014, ESI Vienna (website)

Revised on August 6, 2015 15:55:17 by Urs Schreiber (