On the growth of iterated monodromy groups

Details On the growth of iterated monodromy groups On the growth of iterated monodromy groups

2004-05-24

arxiv.org/abs/math/0405456v2

Mathematics

Group Theory

15 pages, 1 figure. Revised abstract and introduction

Scientific paper

Nekrashevych conjectured that the iterated monodromy groups of quadratic
polynomials with preperiodic critical orbit have intermediate growth. We
illustrate some of the difficulties that arise in attacking this conjecture and
prove subexponential growth for the iterated monodromy group of $z^2+i$. This
is the first non-trivial example supporting the conjecture.

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