• DOI:10.2140/agt.2016.16.675
• Corpus ID: 119630631

Spin structures on loop spaces that characterize string manifolds

@article{Waldorf2012SpinSO,
  title={Spin structures on loop spaces that characterize string manifolds},
  author={Konrad Waldorf},
  journal={arXiv: Algebraic Topology},
  year={2012}
}

• K. Waldorf
• Published 8 September 2012
• Mathematics
• arXiv: Algebraic Topology

Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the loop space of a manifold is spin if and only if the manifold itself is a string manifold, against which it is well-known that only the if-part is true in general. In this article we develop a new version of spin structures on loop spaces that exists if and only if the manifold is string, as desired. This new version consists of a classical spin structure plus a certain fusion product related to loops of frames in the manifold. We use the lifting gerbe theory of Carey-Murray, recent results of Stolz-Teichner on loop spaces, and some own results about string geometry and Brylinski-McLaughlin transgression.