TWISTED COHOMOLOGY AND HOMOLOGY GROUPS ASSOCIATED TO THE RIEMANN-WIRTINGER INTEGRAL.

We study twisted cohomology and homology groups on a onedimensional complex torus minus n distinct points with coefficients in a certain local system of rank one. This local system comes from the integrand of the Riemann-Wirtinger integral introduced by Mano. We construct bases of nonvanishing cohomology and homology groups, give an interpretation as a pairing of a cohomology class and a homology class to the Riemann-Wirtinger integral, and finally describe briefly the Gauss-Manin connection on the cohomology groups. [ABSTRACT FROM AUTHOR]