Nonunique Ergodicity on the Boundary of Outer space

TL;DR

This paper investigates the structure of arational -trees on the boundary of Outer space, focusing on the dimensions of associated simplices of measures and currents, revealing new insights into their geometric properties.

Contribution

It introduces a method to estimate the dimensions of maximal simplices for arational -trees, advancing understanding of boundary structures in Outer space.

Findings

Estimated dimensions of maximal simplices for projective length measures.

Estimated dimensions of maximal simplices for projective dual currents.

Provided new bounds on the complexity of arational -trees.

Abstract

To an $\mathbb{R}$-tree in the boundary of Outer space, we associate two simplices: the simplex of projective length measures, and the simplex of projective dual currents. For both kinds of simplices, we estimate the dimension of maximal simplices for arational $\mathbb{R}$-trees in the boundary of Outer space.