Recent progress of intersection theory for twisted (co)homology groups

Abstract

are the Gamma and the Beta functions. In this paper, we give a geometric meaning for these formulae: If one regards such an integral as the dual pairing between a (kind of) cycle and a (kind of) differential form, then the value given in the right hand side of each formula is the product of the intersection numbers of the two cycles and that of the two forms appeared in the left-hand side. Of course the intersection theory is not made only to explain these well known formulae; for applications, see [CM], [KM], [Yl].