Spin structures on loop spaces that characterize string manifolds

  title={Spin structures on loop spaces that characterize string manifolds},
  author={Konrad Waldorf},
  journal={arXiv: Algebraic Topology},
  • 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… 

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