Miklós Abért: On chains of subgroups and covering towers

Speaker: Miklós Abért

Title: On chains of subgroups and covering towers

Abstract: Let M be a compact manifold and let M_n be a tower of finite sheeted covers of M. What is the natural limit object of M_n? It turns out that when the covers are not regular, this question is not as innocent as it seems, and depending on the choices of basepoints over the covers, one can get to very different answers. In particular, any family of countable residually finite groups can be encoded in such a structure. When one looks at the almost sure choice, it can still be a wide family of limit points, but they are much more related. The full limit information can be encoded into a structure called measurefold, which is the manifold analogue of a graphing.