Abstract
We study a Pfaffian of Appell's hypergeometric system \mathcal F_4 (a,b,c) of differential equations by twisted cohomology groups associated with Euler type integrals representing solutions. We simplify its connection matrix by the pull-back under a double cover of the complement of the singular locus. We express the simplified connection matrix in terms of the intersection form between the twisted cohomology groups.
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