In "Topological vertex" (hepth/0305132), Aganagic, Klemm,
Marino and Vafa conjectured that certain open GromovWitten
invariants of $\C^3$ can be defined for any three partitions
$(\mu_1,\mu_2\mu_3)$ and three integers $(n_1,n_2,n_3)$, and
that such invariants which they call topological
vertex can be used to derive a closed formula of the
generating function of open GromovWitten invariants of toric
CalabiYau threefold.
This talk is to develop a mathematical theory of the topological
vertex.
