We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.

We establish a system of PDE, called open WDVV, that constrains the bulk-deformed superpotential and associated Gromov–Witten invariants Lagrangian submanifold $L \subset X$ with bounding chain. Simultaneously, we define quantum cohomology algebra $X$ relative to $L$ prove its associativity. also connection it is flat. A wall-crossing formula derived allows interchange point-like boundary const...

we investigate the relative cohomology and relative homology theories of $f$-gorenstein modules, consider the relations between classical and $f$-gorenstein (co)homology theories.