Relative twisted homology and cohomology groups associated with Lauricella's \(F_D\) (Q6597286)

In this very technical work the author introduces relative twisted homology and cohomology groups associated with Euler type integrals of solutions to Lauricella's system, i.e., regular holonomic system, \({\mathscr F}_D(a,b,c)\) of hypergeometric differential equations.\N\NThe author defines an intersection form between relative twisted homology groups and that between relative twisted cohomology groups, showing their compatibility.\NHe also proves that the relative twisted homology group is canonically isomorphic to the space of local solutions to \({\mathscr F}_D(a,b,c)\) for any complex parameters \(a\), \(b\), \(c\). Through this isomorphism, he studies the Lauricella's system by the relative twisted homology and cohomology groups and the intersection forms without any conditions on the parameters.