FROBENIUS GROUPS AS MONODROMY GROUPS

Nearly Rational Frobenius Groups

In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.

Alternating groups as monodromy groups in positive characteristic

Let X be a generic curve of genus g defined over an algebraically closed field k of characteristic p ≥ 0. We show that for n sufficiently large there exists a tame rational map f : X → P1k with monodromy group An. This generalizes a result of Magaard–Völklein to positive characteristic.

Hurwitz groups as monodromy groups of dessins: several examples

We present a number of examples to illustrate the use of small quotient dessins as substitutes for their often much larger and more complicated Galois (minimal regular) covers. In doing so we employ several useful group-theoretic techniques, such as the Frobenius character formula for counting triples in a finite group, pointing out some common traps and misconceptions associated with them. Alt...

Iterated Monodromy Groups

We associate a group IMG(f) to every covering f of a topological space M by its open subset. It is the quotient of the fundamental group π1(M) by the intersection of the kernels of its monodromy action for the iterates fn. Every iterated monodromy group comes together with a naturally defined action on a rooted tree. We present an effective method to compute this action and show how the dynamic...

Monodromy Groups and Poincaré Series