WoG 2024 Talk 2.2: Sanghoon Kwak - Nonunique Ergodicity on the Boundary of Outer Space

Speaker: Sanghoon Kwak
Institution: KIAS
Title: Nonunique Ergodicity on the Boundary of Outer Space
Abstract: The Culler--Vogtmann's Outer space $CV_n$ is a space of marked metric graphs, and it
compactifies to a set of $F_n$-trees. Each $F_n$-tree on the boundary of Outer space is equipped with a length measure, and varying length measures on a topological $F_n$-tree gives a simplex in the boundary. The extremal points of the simplex correspond to ergodic length measures. By the results of Gabai and Lenzhen-Masur, the maximal simplex of transverse measures on a fixed filling geodesic lamination on a complete hyperbolic surface of genus $g$ has dimension $3g-4$. In this talk, we give the maximal simplex of length measures on an arational $F_n$-tree has dimension in the interval $[2n-7, 2n-2]$. This is a joint work with Mladen Bestvina, and Elizabeth Field.