Relative symplectic-area independence
= Relative symplectic-area independence
Two homotopy strips with the same endpoint paths and boundary on <Lagrangian submanifolds> glue to a relative $2$-cycle. If that cycle is zero in $H_2(M,L_0\cup L_1)$, its <symplectic area> vanishes: apply <Stokes theorem>, using $d\omega=0$ and the zero restriction of $\omega$ to each Lagrangian. Thus relative homology controls the ambiguity in a <Lagrangian path-area functional>.