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Presented By: Geometry Seminar - Department of Mathematics

Nonunique Ergodicity on the Boundary of Outer space

Sanghoon Kwak

The Culler--Vogtmann's Outer space CVn is a space of marked metric graphs, and it compactifies to a set of Fn-trees. Each Fn-tree on the boundary of Outer space is equipped with a length measure, and varying length measures on a topological Fn-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 Fn-tree has dimension in the interval [2n-7, 2n-2]. This is a joint work with Mladen Bestvina, Jon Chaika, and Elizabeth Field.

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