For the PCF quadratic f(x)=2/(x-1)^2 with strictly pre-periodic critical points, explicit recursive generators for the geometric iterated monodromy group are derived, the arithmetic version is shown to have Hausdorff dimension zero, and maximality of the arboreal Galois group is verifiable at level
Profinite iterated monodromy groups of unicritical polynomials
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A dynamical lifting problem for Galois covers has a negative solution for additive separable polynomials over algebraically closed fields of positive characteristic, together with an explicit dimension formula for the space of linear conjugacy classes containing such polynomials.
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Arboreal Galois Groups of a PCF Map with Strictly Pre-periodic Critical Points
For the PCF quadratic f(x)=2/(x-1)^2 with strictly pre-periodic critical points, explicit recursive generators for the geometric iterated monodromy group are derived, the arithmetic version is shown to have Hausdorff dimension zero, and maximality of the arboreal Galois group is verifiable at level
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A Dynamical Lifting Problem For Additive Polynomials
A dynamical lifting problem for Galois covers has a negative solution for additive separable polynomials over algebraically closed fields of positive characteristic, together with an explicit dimension formula for the space of linear conjugacy classes containing such polynomials.