We study the algebraic conditions leading to chain property of complexes for vertex operator algebra [Formula: see text]-point functions (with their convergence assumed) with differential being defined through reduction formulas. The notion cohomology Riemann surfaces is introduced. Algebraic, geometrical, and cohomological meanings formulas are clarified. A counterpart Bott–Segal theorem in te...

If we have a real vector field in the plane, the integral curves foliate the plane. Similarly, if we have a complex vector field in C then the complex integral curves foliate space by Riemann surfaces. An example of a question one might ask, is whether these Riemann surfaces are dense in space. In the case of vector fields in the plane, this is impossible, but if we do it on a torus instead, it...