On the Poisson relation for compact Lie groups

  title={On the Poisson relation for compact Lie groups},
  author={Craig J. Sutton},
  journal={Annals of Global Analysis and Geometry},
  • Craig J. Sutton
  • Published 23 June 2016
  • Mathematics
  • Annals of Global Analysis and Geometry
Intuition drawn from quantum mechanics and geometric optics raises the following long-standing question: Can the length spectrum of a closed Riemannian manifold be recovered from its Laplace spectrum? By demonstrating that the Poisson relation is an equality for a generic bi-invariant metric on a compact Lie group, we establish that the length spectrum of a generic bi-invariant metric on a compact Lie group can be recovered from its Laplace spectrum. Furthermore, we exhibit a substantial… 
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