Damien Gaboriau, Dynamics on the space of subgroups скачать в хорошем качестве

Damien Gaboriau, Dynamics on the space of subgroups

To every countable group G one can attach a topological object: the space of all its subgroups, denoted Sub(G). It is compact and totally disconnected. The group G acts on this space by conjugation, giving rise to a natural 0-dimensional dynamical system. One can explore this system by peeling away the isolated points of Sub(G) step by step, a process that eventually reveals its perfect kernel and a numerical invariant known as the Cantor–Bendixson rank. In this talk, I will describe what is known about these objects, why they are interesting, and what kinds of dynamics one can observe: from orderly behavior to some phenomena of chaos. Along the way, we will look at concrete families of groups – such as abelian groups, hyperbolic groups and to Baumslag—Solitar groups – where these phenomena can be seen in action. This relies on joint works with P. Azuelos, S. Bontemps, A. Carderi, F. Le Maıtre, and Y. Stalder.