C-spaces, generalized geometry and double field theory

G. Papadopoulos

Published 2014-12-03Version 1

We construct a class of C-spaces associated with closed 3-forms. We show that they depend only on the class of 3-form in $H^3(M, Z)$ and that induce a generalized geometry structure on the spacetime. We also explain their relation to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and at their double overlaps of a spacetime generalizing the standard construction of Kaluza-Klein spaces for 2-forms. C-spaces are not manifolds and satisfy the topological geometrization condition. Double manifolds arise as local subspaces of C-spaces that cannot be globally extended. This indicates that for the global definition of double field theories additional coordinates are needed. We explore several other aspect of C-spaces like their topology and relation to Whitehead towers, and also describe the construction of C-spaces for closed k-forms.