Title: Twisted cohomology and homology groups associated to the Riemann-Wirtinger integral
Abstract:We study twisted cohomology and homology groups on a one-dimensional complex torus minus $n$ distinct points with coefficients in a certain local system of rank one. This local system comes from the i...We study twisted cohomology and homology groups on a one-dimensional 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 non-vanishing 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.Read More