Here are some letters to Alan Weinstein written between 1998 and 2000 about Courant algebroids. Use with care.
All letters with a summary 1 2 3 4 5 6 7 8


  1. definition and classification of exact Courant algebroids (CAs), their origin in 2dim variational problems, a connection with gerbes
  2. review of Poisson-Lie T-duality, the exact CA over a Lie group, Dirac structures as boundary conditions (D-branes)
  3. local description of transitive CAs, connection with central extensions
  4. classification of transitive CAs (via transitive Lie algebroids with vanishing 1st Pontriagin class), reductions of CAs, geometry of Poisson-Lie T-duality
  5. the connection between CAs and gerbes (via conducting bundles)
  6. a canonical construction of a nilpotent Dirac operator generating (any) CA (following A.Alekseev and P.Xu); Clifford and Grassmann algebroids
  7. CA = symplectic dg-manifold with symplectic form of degree 2; the connection between CAs and gerbes via dg manifolds
  8. integration of Lie algebroids/Courant algebroids/bialgebroids/etc. using the ideas of Sullivan's rational homotopy theory and the AKSZ construction of TQFTs (integration=homotopy)