Abstract
We construct a C-space associated with every closed 3-form on a spacetime M and show that it depends on the class of the form in \( {H}^3\left(M,\mathrm{\mathbb{Z}}\right) \). We also demonstrate that C-spaces have a relation to generalized geometry and 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 may not be manifolds and satisfy the topological geometrization condition. Double spaces 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.
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Papadopoulos, G. C-spaces, generalized geometry and double field theory. J. High Energ. Phys. 2015, 29 (2015). https://doi.org/10.1007/JHEP09(2015)029
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DOI: https://doi.org/10.1007/JHEP09(2015)029