Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 2.3.2010 |
| Speaker: | Florian Sobieczky, Mathematical Institute, Friedrich Schiller University of Jena |
| Title: | Amenability of horocyclic products of trees |
| Abstract: | The lamplighter-group on the integers is amenable although is has exponential growth. The Cayley graph of this group with respect to a natural set of generators is the so-called horocyclic product of two homogeneous trees. The talk summarizes results about the stability of amenability of this type of graph under modifications. These include random perturbations (`Percolation', [1, 2]), horocyclic products of periodic, and uniformly growing trees. The latter include `quasi-periodic' trees generated by Sturmian sequences, as well as trees belonging to simple substitution systems. Open questions regarding other types of trees are discussed. |
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