Global aspects of doubled geometry and pre-rackoid

@article{Ikeda2020GlobalAO,
  title={Global aspects of doubled geometry and pre-rackoid},
  author={Noriaki Ikeda and Shin Sasaki},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
The integration problem of a C-bracket and a Vaisman (metric, pre-DFT) algebroid which are geometric structures of double field theory (DFT) is analyzed. We introduce a notion of a pre-rackoid as a global group-like object for an infinitesimal algebroid structure. We propose that several realizations of pre-rackoid structures. One realization is that elements of a pre-rackoid are defined by cotangent paths along doubled foliations in a para-Hermitian manifold. Another realization is proposed as… 

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