Laurent Bartholdi

Thurston equivalence of topological polynomials

We answer Hubbards question on determining the Thurston equivalence class of “twisted rabbits”, i.e. composita of the “rabbit” polynomial with nth powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions.

Branch rings, thinned rings, tree enveloping rings

AbstractWe develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.In particular, for every fieldn

Growth of permutational extensions

Bbbk

Groups of given intermediate word growth@@@Groupes de croissance intermédiaire donnée

n% MathType!End!2!1! we contruct an

On amenability of group algebras, I

Bbbk - algebra

The congruence subgroup problem for branch groups

n% MathType!End!2!1! which• is finitely generated and infinite-dimensional, but has only finitedimensional quotients;• has a subalgebra of finite codimension, isomorphic toM2(k);• is prime;• has quadratic growth, and therefore Gelfand-Kirillov dimension 2;• is recursively presented;• satisfies no identity;• contains a transcendental, invertible element;• is semiprimitive ifn