First of all one needs to define a co-boundary operator formula_72. For CR manifolds that arise as boundaries of complex manifolds, one may view this operator as the restriction of formula_73 from the interior to the boundary. The subscript b is to remind one that we are on the boundary. The co-boundary operator takes (0,p) forms to (0,p+1) forms. One can even define the co-boundary operator for an abstract CR manifold even if it is not the boundary of a complex variety. This can be done using the Webster connection. The co-boundary operator formula_72 forms a complex, that is formula_75. This complex is called the Tangential Cauchy–Riemann complex or the Kohn–Rossi complex. Investigation of this complex and the study of the Cohomology groups of this complex was done in a fundamental paper by Joseph J. Kohn and Hugo Rossi.