L ∞ -Algebra Connections and Applications to String- and Chern-Simons n-Transport

  title={L ∞ -Algebra Connections and Applications to String- and Chern-Simons n-Transport},
  author={Hisham Sati and Urs Schreiber and Jim Stasheff},
  journal={arXiv: Differential Geometry},
We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L ∞-algebras and use it to study the obstruction theory of lifts through higher String-like extensions of Lie algebras. We find (generalized) Chern-Simons and BF-theory functionals this way and describe aspects of their parallel transport and quantization. 
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