Research Fellows Directory
Mr JiaWen Zhang
University of Southampton
I have a Royal Society - Sino British Fellowship Trust Fellowship.
Recently we are working on the problem whether bounded automata groups have finite decomposition complexity (FDC) or not. We know that bounded automata groups can be embedded into one of the mother groups, and we proved that all of the mother groups have infinite asymptotic dimensions and we proved it by two methods. One is to show that the first mother group is coarsely equivalent to the cubic power of itself. Another is more precise: we show that the direct sum of countable infinitely many copies of the integer can be embedded into all of the mother groups. Then we study the decomposition complexity of the mother group. We focus on the decomposition complexity of a special subgroup in the first mother group. We study the commutation relations between the generators, then by induction one can show that this subgroup has FDC.
We are also working on the relation of FDC between a residually finite group and its box spaces. And we have showed some simple relation of FDC with amenability.