Line Bundles over Loop Spaces

  • Jean-Luc Brylinski
Part of the Progress in Mathematics book series (MBC)


The theme of this chapter is that a Dixmier-Douady sheaf of groupoids with connective structure over a manifold M leads naturally to a line bundle over the free loop space LM. This is in complete analogy to the well-known fact that a line bundle with connection over M leads to a function over LM, its holonomy.


Line Bundle Isomorphism Class Boundary Component Central Extension Loop Space 


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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Jean-Luc Brylinski
    • 1
  1. 1.Department of MathematicsThe Penn State UniversityUniversity ParkUSA

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