\times M'$, where $M^-$ denotes the manifold $M$ endowed with the opposite of its symplectic form.

This kind of correspondences, sometimes called canonical relations, appears frequently in symplectic geometry: a diffeomorphism between two symplectic manifolds is a symplectomorphism if and only if its graph is a Lagrangian correspondence. Moreover, given a Hamiltonian group action of a group $G$ on a symplectic manifold $M$ which is free on the zero level on the moment map, the zero level of the moment map induces a Lagrangian correspondence from $M$ to $M{/\!\!/}G$.

Recall the following definition from Wehrheim and Woodward:

A *generalized Lagrangian correspondence* between two symplectic manifolds $M$ and $M'$ consists of intermediate symplectic manifolds $M_1$, $M_2$, ..., $M_{k-1}$, and a sequence of Lagrangian correspondences, for $0\leq i \leq k-1$, $L_{i(i+1)} \subset M_i ^- \times M_{i+1}$, with $M_0 = M$ and $M_k = M'$. Such a sequence will be denoted $\underline{L}$: $$\underline{L} = \left(  \xymatrix{   M_0 \ar[r]^{L_{01}} &  M_1 \ar[r]^{L_{12}} &  M_2 \ar[r]^{L_{23}} & \cdots \ar[r]^{L_{(k-1)k}} & M_k } \right),$$ The integer $k$ will be referred to as the *length of $\underline{L}$*. If $L$ (resp. $\underline{L}$) denotes a (resp. generalized) Lagrangian correspondence from $M$ to $M'$, we will denote $L^T$ (resp. $\underline{L}^T$) 