Here are some letters to Alan Weinstein written between 1998 and 2000. Use with care. 1 2 3 4 5 6 7 8 9 10
contents:
  1. definition and classification of exact Courant algebroids (CAs), their origin in 2dim variational problems, suggested 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
  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)
  9. a double symplectic groupoid via moduli spaces of flat connections
  10. remarks on the problem of calculating H(B Gamma) using the Lie algebroid of Gamma and differential forms