MR2918150 Yoshishige HARAOKA and Katsuhisa MIMACHI Yoshishige HARAOKA and Katsuhisa MIMACHI A Connection Problem for Simpson's Even Family of Rank Four Funkcialaj Ekvacioj. Serio Internacia 54 2011 495--515 http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-3/54_495.pdf http://www.ams.org/mathscinet-getitem?mr=MR2918150 We solve a connection problem for the equation of rank four in Simpson's even family, which we call Even four. We use an integral representation of solutions, and consider the twisted homology group associated with it. The rank of the homology group is five. Its four dimensional subspace, consisting of regularizable cycles, corresponds to the solution space of Even four. The connection problem is reduced to solving the linear relations among twisted cycles. There are only few equations for which connection problems are solved in this way. Simpson's even family, Connection coefficient, Connection problem, Rigid local system. 33C60, 34M40. 54-495 2011 A Connection Problem for Simpson's Even Family of Rank Four Yoshishige HARAOKA and Katsuhisa MIMACHI Yoshishige HARAOKA and Katsuhisa MIMACHI
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