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Monodromy for the Frobenius solution of P6 is in F. V. Andreev

Summary: Monodromy for the Frobenius solution of P6 is in
F. V. Andreev
Western Illinois University
Macomb, IL 61455
E-mail: F-Andreev@wiu.edu
December 19, 2003
A solution to the sixth Painleve equation arising from the theory of
Frobenius manifolds (see work by Manin [16]) is considered. The corre-
sponding monodromy matrices are computed. The author proves that
the resulting monodromy group is conjugate to a subgroup of SL(2, Z).
Short title: Monodromy for the Frobenius solution is in SL(2,Z)
1 Introduction
In year 2000, Alexander Kitaev and the author presented monodromy matri-
ces for (what I will be calling) the Frobenius solution of the sixth Painlev´e
equation (P6) or the Manin's solution because it appears in the book by
Manin [16]. The fact that the method of [1] solved the monodromy problem
for the Manins's solution (see (3) below) was remarkable in itself: precisely


Source: Andreev, Fedor - Department of Mathematics, Western Illinois University


Collections: Mathematics