An important theme in the study of combinatorics of words involves looking for models of nonlinear words, that is words that are not indexed by segments of integers. We discuss one such model arising from the theory of Stallings subgroup graphs. This model naturally leads to the notion of subset currents on free groups (and on other word-hyperbolic groups) which are measure-theoretic analogs of conjugacy classes of finitely generated subgroups. Many new features manifest themselves in this context, including connections with the Hanna Neumann Conjecture and Whitehead’s algorithm for subgroups.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
