Topological groups from matrices of sets

In this talk, I will present a general construction of topological groups from combinatorial structures such as trees, towers, and gaps. Some topological properties of these groups will be determined from the combinatorics of considered objects. For example, the group built from a tree will be a Frechet group if and only if the tree is Aronszajn. The talk is based on a joint work with Stepan Milosevic and Stevo Todorcevic.